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ggplot2 >Statistical >geom_qq
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geom_qq in ggplot2

How to make a quantile-quantile plot in ggplot2 using geom\_qq and geom\_qq\_line.


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Basic geom_qq graph

A quantile-quantile graph is used to determine whether a range of numbers follows a certain distribution: the closer the data points are to being a straight line, the closer the data is to the distribution. (The default distribution is normal.) This dataset gives the daily change in the S&P 500, as well as Apple, Microsoft, IBM, and Starbucks stocks between January 2007 and February 2016.

library(plotly)
stocks <- read.csv("https://raw.githubusercontent.com/plotly/datasets/master/stockdata2.csv",
                   stringsAsFactors = FALSE)

p <- ggplot(stocks, aes(sample=change)) +
  geom_qq()

ggplotly(p)

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Adding geom_qq_line

geom_qq_line provides the 45º angle against which to compare the geom_qq plot. If the two lines match, then the plot matches the distribution. The steeper parts at the ends of the plot suggest that outliers are common in the stock data than would be in a perfect normal distribution (i.e. higher kurtosis).

library(plotly)
stocks <- read.csv("https://raw.githubusercontent.com/plotly/datasets/master/stockdata2.csv",
                   stringsAsFactors = FALSE)

p <- ggplot(stocks, aes(sample=change))+
  geom_qq() + geom_qq_line()

ggplotly(p)

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Comparing Multiple Distributions

We can plot the different stocks using different colours. (Size and opacity are adjusted, and the y-axis shrunk, so that the different curves can be visually distinguished.) We can see that outlier values (both positive and negative) are more common for Starbucks and Apple.

library(plotly)
stocks <- read.csv("https://raw.githubusercontent.com/plotly/datasets/master/stockdata2.csv",
                   stringsAsFactors = FALSE)

p <- ggplot(stocks, aes(sample=change))+
  geom_qq_line() + geom_qq(aes(colour=stock), alpha=0.3, size=0.1) + 
  ylim(-10,10)

ggplotly(p)

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0.0320542132<br />change:  3.205421e-02<br />stock: IBM","theoretical:  0.005437398<br />sample:  0.0329038345<br />change:  3.290383e-02<br />stock: IBM","theoretical:  0.006524892<br />sample:  0.0342974562<br />change:  3.429746e-02<br />stock: IBM","theoretical:  0.007612394<br />sample:  0.0389279432<br />change:  3.892794e-02<br />stock: IBM","theoretical:  0.008699904<br />sample:  0.0451166774<br />change:  4.511668e-02<br />stock: IBM","theoretical:  0.009787425<br />sample:  0.0467513366<br />change:  4.675134e-02<br />stock: IBM","theoretical:  0.010874957<br />sample:  0.0492506773<br />change:  4.925068e-02<br />stock: IBM","theoretical:  0.011962503<br />sample:  0.0510600862<br />change:  5.106009e-02<br />stock: IBM","theoretical:  0.013050062<br />sample:  0.0519515368<br />change:  5.195154e-02<br />stock: IBM","theoretical:  0.014137637<br />sample:  0.0521920119<br />change:  5.219201e-02<br />stock: IBM","theoretical:  0.015225228<br />sample:  0.0530938373<br />change:  5.309384e-02<br />stock: IBM","theoretical:  0.016312838<br />sample:  0.0533310197<br />change:  5.333102e-02<br />stock: IBM","theoretical:  0.017400467<br />sample:  0.0538807741<br />change:  5.388077e-02<br />stock: IBM","theoretical:  0.018488116<br />sample:  0.0541313302<br />change:  5.413133e-02<br />stock: IBM","theoretical:  0.019575788<br />sample:  0.0554746854<br />change:  5.547469e-02<br />stock: IBM","theoretical:  0.020663482<br />sample:  0.0557543121<br />change:  5.575431e-02<br />stock: IBM","theoretical:  0.021751201<br />sample:  0.0562471455<br />change:  5.624715e-02<br />stock: IBM","theoretical:  0.022838946<br />sample:  0.0593921541<br />change:  5.939215e-02<br />stock: IBM","theoretical:  0.023926717<br />sample:  0.0613598673<br />change:  6.135987e-02<br />stock: IBM","theoretical:  0.025014517<br />sample:  0.0614358968<br />change:  6.143590e-02<br />stock: IBM","theoretical:  0.026102347<br />sample:  0.0621442422<br />change:  6.214424e-02<br />stock: IBM","theoretical:  0.027190208<br />sample:  0.0635647773<br />change:  6.356478e-02<br />stock: IBM","theoretical:  0.028278100<br />sample:  0.0655086342<br />change:  6.550863e-02<br />stock: IBM","theoretical:  0.029366026<br />sample:  0.0659187420<br />change:  6.591874e-02<br />stock: IBM","theoretical:  0.030453987<br />sample:  0.0673785634<br />change:  6.737856e-02<br />stock: IBM","theoretical:  0.031541984<br />sample:  0.0675841370<br />change:  6.758414e-02<br />stock: IBM","theoretical:  0.032630019<br />sample:  0.0706541023<br />change:  7.065410e-02<br />stock: IBM","theoretical:  0.033718091<br />sample:  0.0707629413<br />change:  7.076294e-02<br />stock: IBM","theoretical:  0.034806204<br />sample:  0.0708301077<br />change:  7.083011e-02<br />stock: IBM","theoretical:  0.035894358<br />sample:  0.0722354452<br />change:  7.223545e-02<br />stock: IBM","theoretical:  0.036982555<br />sample:  0.0743138467<br />change:  7.431385e-02<br />stock: IBM","theoretical:  0.038070795<br />sample:  0.0759038610<br />change:  7.590386e-02<br />stock: IBM","theoretical:  0.039159081<br />sample:  0.0759341862<br />change:  7.593419e-02<br />stock: IBM","theoretical:  0.040247412<br />sample:  0.0764625098<br />change:  7.646251e-02<br />stock: IBM","theoretical:  0.041335792<br />sample:  0.0803711464<br />change:  8.037115e-02<br />stock: IBM","theoretical:  0.042424220<br />sample:  0.0809289891<br />change:  8.092899e-02<br />stock: IBM","theoretical:  0.043512699<br />sample:  0.0822685220<br />change:  8.226852e-02<br />stock: IBM","theoretical:  0.044601229<br />sample:  0.0880039960<br />change:  8.800400e-02<br />stock: IBM","theoretical:  0.045689813<br />sample:  0.0885650990<br />change:  8.856510e-02<br />stock: IBM","theoretical:  0.046778450<br />sample:  0.0889529988<br />change:  8.895300e-02<br />stock: IBM","theoretical:  0.047867143<br />sample:  0.0932925700<br />change:  9.329257e-02<br />stock: IBM","theoretical:  0.048955892<br />sample:  0.0937181617<br />change:  9.371816e-02<br />stock: IBM","theoretical:  0.050044699<br />sample:  0.0939792221<br />change:  9.397922e-02<br />stock: IBM","theoretical:  0.051133566<br />sample:  0.0949380671<br />change:  9.493807e-02<br />stock: IBM","theoretical:  0.052222494<br />sample:  0.0950601681<br />change:  9.506017e-02<br />stock: IBM","theoretical:  0.053311483<br />sample:  0.0993242637<br />change:  9.932426e-02<br />stock: IBM","theoretical:  0.054400536<br />sample:  0.1001913420<br />change:  1.001913e-01<br />stock: IBM","theoretical:  0.055489653<br />sample:  0.1011119159<br />change:  1.011119e-01<br />stock: IBM","theoretical:  0.056578836<br />sample:  0.1023703673<br />change:  1.023704e-01<br />stock: IBM","theoretical:  0.057668086<br />sample:  0.1032192983<br />change:  1.032193e-01<br />stock: IBM","theoretical:  0.058757404<br />sample:  0.1035648886<br />change:  1.035649e-01<br />stock: IBM","theoretical:  0.059846793<br />sample:  0.1036126425<br />change:  1.036126e-01<br />stock: IBM","theoretical:  0.060936252<br />sample:  0.1038944248<br />change:  1.038944e-01<br />stock: IBM","theoretical:  0.062025783<br />sample:  0.1039375556<br />change:  1.039376e-01<br />stock: IBM","theoretical:  0.063115389<br />sample:  0.1072936203<br />change:  1.072936e-01<br />stock: IBM","theoretical:  0.064205069<br />sample:  0.1077674394<br />change:  1.077674e-01<br />stock: IBM","theoretical:  0.065294825<br />sample:  0.1078728494<br />change:  1.078728e-01<br />stock: IBM","theoretical:  0.066384659<br />sample:  0.1082526671<br />change:  1.082527e-01<br />stock: IBM","theoretical:  0.067474572<br />sample:  0.1084919635<br />change:  1.084920e-01<br />stock: IBM","theoretical:  0.068564565<br />sample:  0.1085348289<br />change:  1.085348e-01<br />stock: IBM","theoretical:  0.069654639<br />sample:  0.1108504757<br />change:  1.108505e-01<br />stock: IBM","theoretical:  0.070744796<br />sample:  0.1129368662<br />change:  1.129369e-01<br />stock: IBM","theoretical:  0.071835038<br />sample:  0.1144653792<br />change:  1.144654e-01<br />stock: IBM","theoretical:  0.072925364<br />sample:  0.1150149314<br />change:  1.150149e-01<br />stock: IBM","theoretical:  0.074015778<br />sample:  0.1157595129<br />change:  1.157595e-01<br />stock: IBM","theoretical:  0.075106279<br />sample:  0.1174596774<br />change:  1.174597e-01<br />stock: IBM","theoretical:  0.076196870<br />sample:  0.1182498235<br />change:  1.182498e-01<br />stock: IBM","theoretical:  0.077287551<br />sample:  0.1187733722<br />change:  1.187734e-01<br />stock: IBM","theoretical:  0.078378325<br />sample:  0.1208896750<br />change:  1.208897e-01<br />stock: IBM","theoretical:  0.079469191<br />sample:  0.1210739829<br />change:  1.210740e-01<br />stock: IBM","theoretical:  0.080560152<br />sample:  0.1217137709<br />change:  1.217138e-01<br />stock: IBM","theoretical:  0.081651209<br />sample:  0.1235603529<br />change:  1.235604e-01<br />stock: IBM","theoretical:  0.082742364<br />sample:  0.1241945828<br />change:  1.241946e-01<br />stock: IBM","theoretical:  0.083833616<br />sample:  0.1243449218<br />change:  1.243449e-01<br />stock: IBM","theoretical:  0.084924969<br />sample:  0.1244402927<br />change:  1.244403e-01<br />stock: IBM","theoretical:  0.086016423<br />sample:  0.1278246192<br />change:  1.278246e-01<br />stock: IBM","theoretical:  0.087107979<br />sample:  0.1290320034<br />change:  1.290320e-01<br />stock: IBM","theoretical:  0.088199639<br />sample:  0.1298971222<br />change:  1.298971e-01<br />stock: IBM","theoretical:  0.089291404<br />sample:  0.1305373669<br />change:  1.305374e-01<br />stock: IBM","theoretical:  0.090383276<br />sample:  0.1305569599<br />change:  1.305570e-01<br />stock: IBM","theoretical:  0.091475255<br />sample:  0.1307510435<br />change:  1.307510e-01<br />stock: IBM","theoretical:  0.092567343<br />sample:  0.1312433892<br />change:  1.312434e-01<br />stock: IBM","theoretical:  0.093659542<br />sample:  0.1358450892<br />change:  1.358451e-01<br />stock: IBM","theoretical:  0.094751853<br />sample:  0.1360461084<br />change:  1.360461e-01<br />stock: IBM","theoretical:  0.095844277<br />sample:  0.1377686611<br />change:  1.377687e-01<br />stock: IBM","theoretical:  0.096936815<br />sample:  0.1399857220<br />change:  1.399857e-01<br />stock: IBM","theoretical:  0.098029468<br />sample:  0.1400316462<br />change:  1.400316e-01<br />stock: IBM","theoretical:  0.099122239<br />sample:  0.1401481237<br />change:  1.401481e-01<br />stock: IBM","theoretical:  0.100215128<br />sample:  0.1408423746<br />change:  1.408424e-01<br />stock: IBM","theoretical:  0.101308137<br />sample:  0.1419399201<br />change:  1.419399e-01<br />stock: IBM","theoretical:  0.102401267<br />sample:  0.1440866354<br />change:  1.440866e-01<br />stock: IBM","theoretical:  0.103494520<br />sample:  0.1441702779<br />change:  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IBM","theoretical:  0.126483460<br />sample:  0.1713274421<br />change:  1.713274e-01<br />stock: IBM","theoretical:  0.127579744<br />sample:  0.1717156384<br />change:  1.717156e-01<br />stock: IBM","theoretical:  0.128676182<br />sample:  0.1727431376<br />change:  1.727431e-01<br />stock: IBM","theoretical:  0.129772774<br />sample:  0.1742140541<br />change:  1.742141e-01<br />stock: IBM","theoretical:  0.130869522<br />sample:  0.1743020819<br />change:  1.743021e-01<br />stock: IBM","theoretical:  0.131966428<br />sample:  0.1766199390<br />change:  1.766199e-01<br />stock: IBM","theoretical:  0.133063493<br />sample:  0.1782436225<br />change:  1.782436e-01<br />stock: IBM","theoretical:  0.134160717<br />sample:  0.1785145207<br />change:  1.785145e-01<br />stock: IBM","theoretical:  0.135258104<br />sample:  0.1791249806<br />change:  1.791250e-01<br />stock: IBM","theoretical:  0.136355653<br />sample:  0.1817204391<br />change:  1.817204e-01<br />stock: IBM","theoretical:  0.137453366<br />sample:  0.1824508108<br />change:  1.824508e-01<br />stock: IBM","theoretical:  0.138551245<br />sample:  0.1832852698<br />change:  1.832853e-01<br />stock: IBM","theoretical:  0.139649291<br />sample:  0.1839409641<br />change:  1.839410e-01<br />stock: IBM","theoretical:  0.140747506<br />sample:  0.1854323113<br />change:  1.854323e-01<br />stock: IBM","theoretical:  0.141845890<br />sample:  0.1856150617<br />change:  1.856151e-01<br />stock: IBM","theoretical:  0.142944446<br />sample:  0.1867420397<br />change:  1.867420e-01<br />stock: IBM","theoretical:  0.144043174<br />sample:  0.1887129940<br />change:  1.887130e-01<br />stock: IBM","theoretical:  0.145142076<br />sample:  0.1892078690<br />change:  1.892079e-01<br />stock: IBM","theoretical:  0.146241153<br />sample:  0.1894151447<br />change:  1.894151e-01<br />stock: IBM","theoretical:  0.147340407<br />sample:  0.1903476909<br />change:  1.903477e-01<br />stock: IBM","theoretical:  0.148439839<br />sample:  0.1914148508<br />change:  1.914149e-01<br />stock: IBM","theoretical:  0.149539450<br />sample:  0.1927825834<br />change:  1.927826e-01<br />stock: IBM","theoretical:  0.150639242<br />sample:  0.1934654969<br />change:  1.934655e-01<br />stock: IBM","theoretical:  0.151739217<br />sample:  0.1941926581<br />change:  1.941927e-01<br />stock: IBM","theoretical:  0.152839375<br />sample:  0.1942542763<br />change:  1.942543e-01<br />stock: IBM","theoretical:  0.153939718<br />sample:  0.1958381628<br />change:  1.958382e-01<br />stock: IBM","theoretical:  0.155040248<br />sample:  0.1961069087<br />change:  1.961069e-01<br />stock: IBM","theoretical:  0.156140965<br />sample:  0.1977954276<br />change:  1.977954e-01<br />stock: IBM","theoretical:  0.157241872<br />sample:  0.1985058368<br />change:  1.985058e-01<br />stock: IBM","theoretical:  0.158342969<br />sample:  0.1990890663<br />change:  1.990891e-01<br />stock: IBM","theoretical:  0.159444258<br />sample:  0.1998821754<br />change:  1.998822e-01<br />stock: IBM","theoretical:  0.160545741<br />sample:  0.2005912193<br />change:  2.005912e-01<br />stock: IBM","theoretical:  0.161647418<br />sample:  0.2009011357<br />change:  2.009011e-01<br />stock: IBM","theoretical:  0.162749292<br />sample:  0.2022799871<br />change:  2.022800e-01<br />stock: IBM","theoretical:  0.163851363<br />sample:  0.2029470344<br />change:  2.029470e-01<br />stock: IBM","theoretical:  0.164953633<br />sample:  0.2035908793<br />change:  2.035909e-01<br />stock: IBM","theoretical:  0.166056104<br />sample:  0.2055847149<br />change:  2.055847e-01<br />stock: IBM","theoretical:  0.167158777<br />sample:  0.2056341845<br />change:  2.056342e-01<br />stock: IBM","theoretical:  0.168261653<br />sample:  0.2067403307<br />change:  2.067403e-01<br />stock: IBM","theoretical:  0.169364733<br />sample:  0.2070194481<br />change:  2.070194e-01<br />stock: IBM","theoretical:  0.170468020<br />sample:  0.2072289274<br />change:  2.072289e-01<br />stock: IBM","theoretical:  0.171571514<br />sample:  0.2072734573<br />change:  2.072735e-01<br />stock: IBM","theoretical:  0.172675218<br />sample:  0.2094477171<br />change:  2.094477e-01<br />stock: IBM","theoretical:  0.173779131<br />sample:  0.2096998372<br />change:  2.096998e-01<br />stock: IBM","theoretical:  0.174883257<br />sample:  0.2114200906<br />change:  2.114201e-01<br />stock: IBM","theoretical:  0.175987596<br />sample:  0.2154235221<br />change:  2.154235e-01<br />stock: IBM","theoretical:  0.177092149<br />sample:  0.2163566711<br />change:  2.163567e-01<br />stock: IBM","theoretical:  0.178196918<br />sample:  0.2180640622<br />change:  2.180641e-01<br />stock: IBM","theoretical:  0.179301905<br />sample:  0.2182143297<br />change:  2.182143e-01<br />stock: IBM","theoretical:  0.180407111<br />sample:  0.2188426053<br />change:  2.188426e-01<br />stock: IBM","theoretical:  0.181512538<br />sample:  0.2206273278<br />change:  2.206273e-01<br />stock: IBM","theoretical:  0.182618186<br />sample:  0.2220804835<br />change:  2.220805e-01<br />stock: IBM","theoretical:  0.183724058<br />sample:  0.2236585909<br />change:  2.236586e-01<br />stock: IBM","theoretical:  0.184830154<br />sample:  0.2237247897<br />change:  2.237248e-01<br />stock: IBM","theoretical:  0.185936476<br />sample:  0.2278121871<br />change:  2.278122e-01<br />stock: IBM","theoretical:  0.187043026<br />sample:  0.2283813207<br />change:  2.283813e-01<br />stock: IBM","theoretical:  0.188149805<br />sample:  0.2294230493<br />change:  2.294230e-01<br />stock: IBM","theoretical:  0.189256815<br />sample:  0.2319690177<br />change:  2.319690e-01<br />stock: IBM","theoretical:  0.190364057<br />sample:  0.2331220085<br />change:  2.331220e-01<br />stock: IBM","theoretical:  0.191471532<br />sample:  0.2343998400<br />change:  2.343998e-01<br />stock: IBM","theoretical:  0.192579242<br />sample:  0.2345869041<br />change:  2.345869e-01<br 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IBM","theoretical:  0.204779973<br />sample:  0.2545826789<br />change:  2.545827e-01<br />stock: IBM","theoretical:  0.205890616<br />sample:  0.2570164723<br />change:  2.570165e-01<br />stock: IBM","theoretical:  0.207001513<br />sample:  0.2585474814<br />change:  2.585475e-01<br />stock: IBM","theoretical:  0.208112666<br />sample:  0.2590567532<br />change:  2.590568e-01<br />stock: IBM","theoretical:  0.209224075<br />sample:  0.2606596765<br />change:  2.606597e-01<br />stock: IBM","theoretical:  0.210335744<br />sample:  0.2621928326<br />change:  2.621928e-01<br />stock: IBM","theoretical:  0.211447672<br />sample:  0.2628698605<br />change:  2.628699e-01<br />stock: IBM","theoretical:  0.212559861<br />sample:  0.2633719437<br />change:  2.633719e-01<br />stock: IBM","theoretical:  0.213672314<br />sample:  0.2635023510<br />change:  2.635024e-01<br />stock: IBM","theoretical:  0.214785031<br />sample:  0.2655737338<br />change:  2.655737e-01<br />stock: IBM","theoretical:  0.215898014<br />sample:  0.2664600286<br />change:  2.664600e-01<br />stock: IBM","theoretical:  0.217011265<br />sample:  0.2671797307<br />change:  2.671797e-01<br />stock: IBM","theoretical:  0.218124784<br />sample:  0.2672776551<br />change:  2.672777e-01<br />stock: IBM","theoretical:  0.219238574<br />sample:  0.2675885796<br />change:  2.675886e-01<br />stock: IBM","theoretical:  0.220352637<br />sample:  0.2690556479<br />change:  2.690556e-01<br />stock: IBM","theoretical:  0.221466972<br />sample:  0.2704982290<br />change:  2.704982e-01<br />stock: IBM","theoretical:  0.222581583<br />sample:  0.2727107821<br />change:  2.727108e-01<br />stock: IBM","theoretical:  0.223696471<br />sample:  0.2748670517<br />change:  2.748671e-01<br />stock: IBM","theoretical:  0.224811636<br />sample:  0.2759866036<br />change:  2.759866e-01<br />stock: IBM","theoretical:  0.225927081<br />sample:  0.2767114074<br />change:  2.767114e-01<br />stock: IBM","theoretical:  0.227042808<br 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0.2911800924<br />change:  2.911801e-01<br />stock: IBM","theoretical:  0.239334795<br />sample:  0.2962330018<br />change:  2.962330e-01<br />stock: IBM","theoretical:  0.240454015<br />sample:  0.2968203195<br />change:  2.968203e-01<br />stock: IBM","theoretical:  0.241573537<br />sample:  0.3005052084<br />change:  3.005052e-01<br />stock: IBM","theoretical:  0.242693362<br />sample:  0.3010735638<br />change:  3.010736e-01<br />stock: IBM","theoretical:  0.243813491<br />sample:  0.3021216149<br />change:  3.021216e-01<br />stock: IBM","theoretical:  0.244933926<br />sample:  0.3027430056<br />change:  3.027430e-01<br />stock: IBM","theoretical:  0.246054669<br />sample:  0.3042473899<br />change:  3.042474e-01<br />stock: IBM","theoretical:  0.247175721<br />sample:  0.3075629994<br />change:  3.075630e-01<br />stock: IBM","theoretical:  0.248297084<br />sample:  0.3088973019<br />change:  3.088973e-01<br />stock: IBM","theoretical:  0.249418759<br />sample:  0.3102590271<br />change:  3.102590e-01<br />stock: IBM","theoretical:  0.250540747<br />sample:  0.3113090363<br />change:  3.113090e-01<br />stock: IBM","theoretical:  0.251663052<br />sample:  0.3117457615<br />change:  3.117458e-01<br />stock: IBM","theoretical:  0.252785673<br />sample:  0.3124071217<br />change:  3.124071e-01<br />stock: IBM","theoretical:  0.253908613<br />sample:  0.3140971213<br />change:  3.140971e-01<br />stock: IBM","theoretical:  0.255031873<br />sample:  0.3143677848<br />change:  3.143678e-01<br />stock: IBM","theoretical:  0.256155456<br />sample:  0.3166745385<br />change:  3.166745e-01<br />stock: IBM","theoretical:  0.257279361<br />sample:  0.3192901792<br />change:  3.192902e-01<br />stock: IBM","theoretical:  0.258403592<br />sample:  0.3196853593<br />change:  3.196854e-01<br />stock: IBM","theoretical:  0.259528149<br />sample:  0.3203183470<br />change:  3.203183e-01<br />stock: IBM","theoretical:  0.260653035<br />sample:  0.3204836687<br />change:  3.204837e-01<br />stock: IBM","theoretical:  0.261778251<br />sample:  0.3213377652<br />change:  3.213378e-01<br />stock: IBM","theoretical:  0.262903798<br />sample:  0.3217800375<br />change:  3.217800e-01<br />stock: IBM","theoretical:  0.264029678<br />sample:  0.3222087107<br />change:  3.222087e-01<br />stock: IBM","theoretical:  0.265155894<br />sample:  0.3227591533<br />change:  3.227592e-01<br />stock: IBM","theoretical:  0.266282445<br />sample:  0.3229417540<br />change:  3.229418e-01<br />stock: IBM","theoretical:  0.267409335<br />sample:  0.3249632975<br />change:  3.249633e-01<br />stock: IBM","theoretical:  0.268536564<br />sample:  0.3249777568<br />change:  3.249778e-01<br />stock: IBM","theoretical:  0.269664135<br />sample:  0.3256114035<br />change:  3.256114e-01<br />stock: IBM","theoretical:  0.270792048<br />sample:  0.3265160476<br />change:  3.265160e-01<br />stock: IBM","theoretical:  0.271920306<br />sample:  0.3266051533<br />change:  3.266052e-01<br />stock: IBM","theoretical:  0.273048911<br />sample:  0.3275858177<br />change:  3.275858e-01<br />stock: IBM","theoretical:  0.274177863<br />sample:  0.3288743802<br />change:  3.288744e-01<br />stock: IBM","theoretical:  0.275307165<br />sample:  0.3296251023<br />change:  3.296251e-01<br />stock: IBM","theoretical:  0.276436818<br />sample:  0.3333378403<br />change:  3.333378e-01<br />stock: IBM","theoretical:  0.277566824<br />sample:  0.3413505673<br />change:  3.413506e-01<br />stock: IBM","theoretical:  0.278697184<br />sample:  0.3427239850<br />change:  3.427240e-01<br />stock: IBM","theoretical:  0.279827901<br />sample:  0.3434316285<br />change:  3.434316e-01<br />stock: IBM","theoretical:  0.280958976<br />sample:  0.3438939382<br />change:  3.438939e-01<br />stock: IBM","theoretical:  0.282090410<br />sample:  0.3466651446<br />change:  3.466651e-01<br />stock: IBM","theoretical:  0.283222205<br />sample:  0.3488523947<br />change:  3.488524e-01<br />stock: IBM","theoretical:  0.284354364<br />sample:  0.3488956123<br />change:  3.488956e-01<br />stock: IBM","theoretical:  0.285486886<br />sample:  0.3490483427<br />change:  3.490483e-01<br />stock: IBM","theoretical:  0.286619776<br />sample:  0.3491350823<br />change:  3.491351e-01<br />stock: IBM","theoretical:  0.287753033<br />sample:  0.3495279204<br />change:  3.495279e-01<br />stock: IBM","theoretical:  0.288886660<br />sample:  0.3500600695<br />change:  3.500601e-01<br />stock: IBM","theoretical:  0.290020658<br />sample:  0.3527137756<br />change:  3.527138e-01<br />stock: IBM","theoretical:  0.291155029<br />sample:  0.3595491000<br />change:  3.595491e-01<br />stock: IBM","theoretical:  0.292289775<br />sample:  0.3600067857<br />change:  3.600068e-01<br />stock: IBM","theoretical:  0.293424898<br />sample:  0.3600892095<br />change:  3.600892e-01<br />stock: IBM","theoretical:  0.294560398<br />sample:  0.3603635754<br />change:  3.603636e-01<br />stock: IBM","theoretical:  0.295696279<br />sample:  0.3610719194<br />change:  3.610719e-01<br />stock: IBM","theoretical:  0.296832541<br />sample:  0.3611023726<br />change:  3.611024e-01<br />stock: IBM","theoretical:  0.297969187<br />sample:  0.3628162423<br />change:  3.628162e-01<br />stock: IBM","theoretical:  0.299106218<br />sample:  0.3636741791<br />change:  3.636742e-01<br />stock: IBM","theoretical:  0.300243635<br />sample:  0.3644675383<br />change:  3.644675e-01<br />stock: IBM","theoretical:  0.301381442<br />sample:  0.3647585559<br />change:  3.647586e-01<br />stock: IBM","theoretical:  0.302519638<br />sample:  0.3653137279<br />change:  3.653137e-01<br />stock: IBM","theoretical:  0.303658227<br />sample:  0.3654888198<br />change:  3.654888e-01<br />stock: IBM","theoretical:  0.304797209<br />sample:  0.3670610859<br />change:  3.670611e-01<br />stock: IBM","theoretical:  0.305936587<br />sample:  0.3683424516<br />change:  3.683425e-01<br />stock: IBM","theoretical:  0.307076362<br 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0.3852702565<br />change:  3.852703e-01<br />stock: IBM","theoretical:  0.319640616<br />sample:  0.3887808488<br />change:  3.887808e-01<br />stock: IBM","theoretical:  0.320785298<br />sample:  0.3908364409<br />change:  3.908364e-01<br />stock: IBM","theoretical:  0.321930399<br />sample:  0.3918014208<br />change:  3.918014e-01<br />stock: IBM","theoretical:  0.323075923<br />sample:  0.3921976201<br />change:  3.921976e-01<br />stock: IBM","theoretical:  0.324221871<br />sample:  0.3929848534<br />change:  3.929849e-01<br />stock: IBM","theoretical:  0.325368245<br />sample:  0.3930060962<br />change:  3.930061e-01<br />stock: IBM","theoretical:  0.326515046<br />sample:  0.3938866427<br />change:  3.938866e-01<br />stock: IBM","theoretical:  0.327662278<br />sample:  0.3947934920<br />change:  3.947935e-01<br />stock: IBM","theoretical:  0.328809940<br />sample:  0.3953577808<br />change:  3.953578e-01<br />stock: IBM","theoretical:  0.329958036<br />sample:  0.3958409362<br />change:  3.958409e-01<br />stock: IBM","theoretical:  0.331106567<br />sample:  0.3959415826<br />change:  3.959416e-01<br />stock: IBM","theoretical:  0.332255535<br />sample:  0.3967098330<br />change:  3.967098e-01<br />stock: IBM","theoretical:  0.333404942<br />sample:  0.3970884931<br />change:  3.970885e-01<br />stock: IBM","theoretical:  0.334554789<br />sample:  0.4003158615<br />change:  4.003159e-01<br />stock: IBM","theoretical:  0.335705079<br />sample:  0.4005223270<br />change:  4.005223e-01<br />stock: IBM","theoretical:  0.336855813<br />sample:  0.4010211405<br />change:  4.010211e-01<br />stock: IBM","theoretical:  0.338006994<br />sample:  0.4022205774<br />change:  4.022206e-01<br />stock: IBM","theoretical:  0.339158622<br />sample:  0.4026498950<br />change:  4.026499e-01<br />stock: IBM","theoretical:  0.340310701<br />sample:  0.4053835600<br />change:  4.053836e-01<br />stock: IBM","theoretical:  0.341463231<br />sample:  0.4054160246<br />change:  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0.377426289<br />sample:  0.4420440904<br />change:  4.420441e-01<br />stock: IBM","theoretical:  0.378594302<br />sample:  0.4422539560<br />change:  4.422540e-01<br />stock: IBM","theoretical:  0.379762832<br />sample:  0.4431343908<br />change:  4.431344e-01<br />stock: IBM","theoretical:  0.380931880<br />sample:  0.4439136904<br />change:  4.439137e-01<br />stock: IBM","theoretical:  0.382101449<br />sample:  0.4442716750<br />change:  4.442717e-01<br />stock: IBM","theoretical:  0.383271541<br />sample:  0.4447789660<br />change:  4.447790e-01<br />stock: IBM","theoretical:  0.384442158<br />sample:  0.4470461659<br />change:  4.470462e-01<br />stock: IBM","theoretical:  0.385613302<br />sample:  0.4470689487<br />change:  4.470689e-01<br />stock: IBM","theoretical:  0.386784975<br />sample:  0.4470780698<br />change:  4.470781e-01<br />stock: IBM","theoretical:  0.387957180<br />sample:  0.4495878261<br />change:  4.495878e-01<br />stock: IBM","theoretical:  0.389129917<br 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0.4612339281<br />change:  4.612339e-01<br />stock: IBM","theoretical:  0.402065836<br />sample:  0.4612826950<br />change:  4.612827e-01<br />stock: IBM","theoretical:  0.403245139<br />sample:  0.4614119638<br />change:  4.614120e-01<br />stock: IBM","theoretical:  0.404425003<br />sample:  0.4631864660<br />change:  4.631865e-01<br />stock: IBM","theoretical:  0.405605431<br />sample:  0.4651209474<br />change:  4.651209e-01<br />stock: IBM","theoretical:  0.406786424<br />sample:  0.4688524662<br />change:  4.688525e-01<br />stock: IBM","theoretical:  0.407967984<br />sample:  0.4727730065<br />change:  4.727730e-01<br />stock: IBM","theoretical:  0.409150114<br />sample:  0.4751165181<br />change:  4.751165e-01<br />stock: IBM","theoretical:  0.410332817<br />sample:  0.4756549749<br />change:  4.756550e-01<br />stock: IBM","theoretical:  0.411516093<br />sample:  0.4773487640<br />change:  4.773488e-01<br />stock: IBM","theoretical:  0.412699946<br />sample:  0.4779735186<br 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4.927373e-01<br />stock: IBM","theoretical:  0.425761017<br />sample:  0.4932156224<br />change:  4.932156e-01<br />stock: IBM","theoretical:  0.426951963<br />sample:  0.4940255403<br />change:  4.940255e-01<br />stock: IBM","theoretical:  0.428143514<br />sample:  0.4954736380<br />change:  4.954736e-01<br />stock: IBM","theoretical:  0.429335674<br />sample:  0.4955421804<br />change:  4.955422e-01<br />stock: IBM","theoretical:  0.430528445<br />sample:  0.4966008868<br />change:  4.966009e-01<br />stock: IBM","theoretical:  0.431721828<br />sample:  0.4975125873<br />change:  4.975126e-01<br />stock: IBM","theoretical:  0.432915826<br />sample:  0.4976827772<br />change:  4.976828e-01<br />stock: IBM","theoretical:  0.434110442<br />sample:  0.4978987235<br />change:  4.978987e-01<br />stock: IBM","theoretical:  0.435305678<br />sample:  0.4990848803<br />change:  4.990849e-01<br />stock: IBM","theoretical:  0.436501536<br />sample:  0.5000039937<br />change:  5.000040e-01<br 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IBM","theoretical:  0.449697719<br />sample:  0.5171058706<br />change:  5.171059e-01<br />stock: IBM","theoretical:  0.450901229<br />sample:  0.5184866168<br />change:  5.184866e-01<br />stock: IBM","theoretical:  0.452105393<br />sample:  0.5219684519<br />change:  5.219685e-01<br />stock: IBM","theoretical:  0.453310213<br />sample:  0.5220657765<br />change:  5.220658e-01<br />stock: IBM","theoretical:  0.454515691<br />sample:  0.5228354934<br />change:  5.228355e-01<br />stock: IBM","theoretical:  0.455721830<br />sample:  0.5263836239<br />change:  5.263836e-01<br />stock: IBM","theoretical:  0.456928633<br />sample:  0.5272717277<br />change:  5.272717e-01<br />stock: IBM","theoretical:  0.458136101<br />sample:  0.5306147319<br />change:  5.306147e-01<br />stock: IBM","theoretical:  0.459344238<br />sample:  0.5322068477<br />change:  5.322068e-01<br />stock: IBM","theoretical:  0.460553045<br />sample:  0.5331958945<br />change:  5.331959e-01<br />stock: IBM","theoretical:  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IBM","theoretical:  0.536919515<br />sample:  0.6221439169<br />change:  6.221439e-01<br />stock: IBM","theoretical:  0.538176023<br />sample:  0.6221622711<br />change:  6.221623e-01<br />stock: IBM","theoretical:  0.539433382<br />sample:  0.6222863159<br />change:  6.222863e-01<br />stock: IBM","theoretical:  0.540691594<br />sample:  0.6243131072<br />change:  6.243131e-01<br />stock: IBM","theoretical:  0.541950662<br />sample:  0.6252434370<br />change:  6.252434e-01<br />stock: IBM","theoretical:  0.543210591<br />sample:  0.6264482668<br />change:  6.264483e-01<br />stock: IBM","theoretical:  0.544471382<br />sample:  0.6283216138<br />change:  6.283216e-01<br />stock: IBM","theoretical:  0.545733039<br />sample:  0.6319372531<br />change:  6.319373e-01<br />stock: IBM","theoretical:  0.546995565<br />sample:  0.6384249022<br />change:  6.384249e-01<br />stock: IBM","theoretical:  0.548258964<br />sample:  0.6399097891<br />change:  6.399098e-01<br />stock: IBM","theoretical:  0.549523239<br />sample:  0.6409555292<br />change:  6.409555e-01<br />stock: IBM","theoretical:  0.550788393<br />sample:  0.6460502234<br />change:  6.460502e-01<br />stock: IBM","theoretical:  0.552054429<br />sample:  0.6473827910<br />change:  6.473828e-01<br />stock: IBM","theoretical:  0.553321350<br />sample:  0.6480020144<br />change:  6.480020e-01<br />stock: IBM","theoretical:  0.554589160<br />sample:  0.6480250999<br />change:  6.480251e-01<br />stock: IBM","theoretical:  0.555857863<br />sample:  0.6497928892<br />change:  6.497929e-01<br />stock: IBM","theoretical:  0.557127460<br />sample:  0.6506804290<br />change:  6.506804e-01<br />stock: IBM","theoretical:  0.558397956<br />sample:  0.6519343617<br />change:  6.519344e-01<br />stock: IBM","theoretical:  0.559669354<br />sample:  0.6530515581<br />change:  6.530516e-01<br />stock: IBM","theoretical:  0.560941658<br />sample:  0.6571202088<br />change:  6.571202e-01<br />stock: IBM","theoretical:  0.562214870<br 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0.6761732570<br />change:  6.761733e-01<br />stock: IBM","theoretical:  0.576281149<br />sample:  0.6773658159<br />change:  6.773658e-01<br />stock: IBM","theoretical:  0.577565531<br />sample:  0.6780536693<br />change:  6.780537e-01<br />stock: IBM","theoretical:  0.578850868<br />sample:  0.6806427517<br />change:  6.806428e-01<br />stock: IBM","theoretical:  0.580137161<br />sample:  0.6894667599<br />change:  6.894668e-01<br />stock: IBM","theoretical:  0.581424414<br />sample:  0.6898219089<br />change:  6.898219e-01<br />stock: IBM","theoretical:  0.582712632<br />sample:  0.6903503747<br />change:  6.903504e-01<br />stock: IBM","theoretical:  0.584001818<br />sample:  0.6925751272<br />change:  6.925751e-01<br />stock: IBM","theoretical:  0.585291975<br />sample:  0.6926488225<br />change:  6.926488e-01<br />stock: IBM","theoretical:  0.586583107<br />sample:  0.6933349953<br />change:  6.933350e-01<br />stock: IBM","theoretical:  0.587875217<br />sample:  0.6934291624<br />change:  6.934292e-01<br />stock: IBM","theoretical:  0.589168310<br />sample:  0.6940514450<br />change:  6.940514e-01<br />stock: IBM","theoretical:  0.590462389<br />sample:  0.6947963184<br />change:  6.947963e-01<br />stock: IBM","theoretical:  0.591757457<br />sample:  0.6970429797<br />change:  6.970430e-01<br />stock: IBM","theoretical:  0.593053518<br />sample:  0.6981366204<br />change:  6.981366e-01<br />stock: IBM","theoretical:  0.594350577<br />sample:  0.6982649223<br />change:  6.982649e-01<br />stock: IBM","theoretical:  0.595648636<br />sample:  0.6987275682<br />change:  6.987276e-01<br />stock: IBM","theoretical:  0.596947700<br />sample:  0.6993935747<br />change:  6.993936e-01<br />stock: IBM","theoretical:  0.598247771<br />sample:  0.6994378015<br />change:  6.994378e-01<br />stock: IBM","theoretical:  0.599548855<br />sample:  0.6995202621<br />change:  6.995203e-01<br />stock: IBM","theoretical:  0.600850954<br />sample:  0.7030864632<br />change:  7.030865e-01<br />stock: IBM","theoretical:  0.602154073<br />sample:  0.7035913574<br />change:  7.035914e-01<br />stock: IBM","theoretical:  0.603458215<br />sample:  0.7045161977<br />change:  7.045162e-01<br />stock: IBM","theoretical:  0.604763385<br />sample:  0.7045995548<br />change:  7.045996e-01<br />stock: IBM","theoretical:  0.606069585<br />sample:  0.7073025577<br />change:  7.073026e-01<br />stock: IBM","theoretical:  0.607376821<br />sample:  0.7079093223<br />change:  7.079093e-01<br />stock: IBM","theoretical:  0.608685095<br />sample:  0.7098793261<br />change:  7.098793e-01<br />stock: IBM","theoretical:  0.609994411<br />sample:  0.7138962134<br />change:  7.138962e-01<br />stock: IBM","theoretical:  0.611304774<br />sample:  0.7160416132<br />change:  7.160416e-01<br />stock: IBM","theoretical:  0.612616188<br />sample:  0.7171665257<br />change:  7.171665e-01<br />stock: IBM","theoretical:  0.613928656<br />sample:  0.7183649419<br />change:  7.183649e-01<br 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IBM","theoretical:  0.628436543<br />sample:  0.7352198142<br />change:  7.352198e-01<br />stock: IBM","theoretical:  0.629761978<br />sample:  0.7358785189<br />change:  7.358785e-01<br />stock: IBM","theoretical:  0.631088521<br />sample:  0.7363520933<br />change:  7.363521e-01<br />stock: IBM","theoretical:  0.632416175<br />sample:  0.7371468296<br />change:  7.371468e-01<br />stock: IBM","theoretical:  0.633744944<br />sample:  0.7377826189<br />change:  7.377826e-01<br />stock: IBM","theoretical:  0.635074834<br />sample:  0.7394303808<br />change:  7.394304e-01<br />stock: IBM","theoretical:  0.636405847<br />sample:  0.7399311047<br />change:  7.399311e-01<br />stock: IBM","theoretical:  0.637737990<br />sample:  0.7426097489<br />change:  7.426097e-01<br />stock: IBM","theoretical:  0.639071264<br />sample:  0.7429237872<br />change:  7.429238e-01<br />stock: IBM","theoretical:  0.640405676<br />sample:  0.7431120498<br />change:  7.431120e-01<br />stock: IBM","theoretical:  0.641741229<br />sample:  0.7440339595<br />change:  7.440340e-01<br />stock: IBM","theoretical:  0.643077928<br />sample:  0.7465934375<br />change:  7.465934e-01<br />stock: IBM","theoretical:  0.644415777<br />sample:  0.7472613751<br />change:  7.472614e-01<br />stock: IBM","theoretical:  0.645754780<br />sample:  0.7478961509<br />change:  7.478962e-01<br />stock: IBM","theoretical:  0.647094942<br />sample:  0.7491285352<br />change:  7.491285e-01<br />stock: IBM","theoretical:  0.648436267<br />sample:  0.7516548552<br />change:  7.516549e-01<br />stock: IBM","theoretical:  0.649778760<br />sample:  0.7518785569<br />change:  7.518786e-01<br />stock: IBM","theoretical:  0.651122424<br />sample:  0.7522864586<br />change:  7.522865e-01<br />stock: IBM","theoretical:  0.652467266<br />sample:  0.7525469150<br />change:  7.525469e-01<br />stock: IBM","theoretical:  0.653813289<br />sample:  0.7534653468<br />change:  7.534653e-01<br />stock: IBM","theoretical:  0.655160497<br 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0.7670343699<br />change:  7.670344e-01<br />stock: IBM","theoretical:  0.670059350<br />sample:  0.7687172503<br />change:  7.687173e-01<br />stock: IBM","theoretical:  0.671421146<br />sample:  0.7712370309<br />change:  7.712370e-01<br />stock: IBM","theoretical:  0.672784188<br />sample:  0.7712750154<br />change:  7.712750e-01<br />stock: IBM","theoretical:  0.674148481<br />sample:  0.7721660314<br />change:  7.721660e-01<br />stock: IBM","theoretical:  0.675514030<br />sample:  0.7744494073<br />change:  7.744494e-01<br />stock: IBM","theoretical:  0.676880840<br />sample:  0.7768683068<br />change:  7.768683e-01<br />stock: IBM","theoretical:  0.678248915<br />sample:  0.7793730407<br />change:  7.793730e-01<br />stock: IBM","theoretical:  0.679618261<br />sample:  0.7807363488<br />change:  7.807363e-01<br />stock: IBM","theoretical:  0.680988883<br />sample:  0.7928257093<br />change:  7.928257e-01<br />stock: IBM","theoretical:  0.682360785<br />sample:  0.7928999377<br />change:  7.928999e-01<br />stock: IBM","theoretical:  0.683733972<br />sample:  0.7935634974<br />change:  7.935635e-01<br />stock: IBM","theoretical:  0.685108451<br />sample:  0.7954883779<br />change:  7.954884e-01<br />stock: IBM","theoretical:  0.686484224<br />sample:  0.7963477883<br />change:  7.963478e-01<br />stock: IBM","theoretical:  0.687861298<br />sample:  0.7967051293<br />change:  7.967051e-01<br />stock: IBM","theoretical:  0.689239678<br />sample:  0.7978414830<br />change:  7.978415e-01<br />stock: IBM","theoretical:  0.690619369<br />sample:  0.7986593237<br />change:  7.986593e-01<br />stock: IBM","theoretical:  0.692000375<br />sample:  0.7991171472<br />change:  7.991171e-01<br />stock: IBM","theoretical:  0.693382703<br />sample:  0.8002722504<br />change:  8.002723e-01<br />stock: IBM","theoretical:  0.694766357<br />sample:  0.8050183040<br />change:  8.050183e-01<br />stock: IBM","theoretical:  0.696151342<br />sample:  0.8100029704<br />change:  8.100030e-01<br />stock: IBM","theoretical:  0.697537663<br />sample:  0.8112928540<br />change:  8.112929e-01<br />stock: IBM","theoretical:  0.698925327<br />sample:  0.8139734420<br />change:  8.139734e-01<br />stock: IBM","theoretical:  0.700314338<br />sample:  0.8155354231<br />change:  8.155354e-01<br />stock: IBM","theoretical:  0.701704701<br />sample:  0.8158261371<br />change:  8.158261e-01<br />stock: IBM","theoretical:  0.703096422<br />sample:  0.8202685719<br />change:  8.202686e-01<br />stock: IBM","theoretical:  0.704489507<br />sample:  0.8252769190<br />change:  8.252769e-01<br />stock: IBM","theoretical:  0.705883959<br />sample:  0.8270960651<br />change:  8.270961e-01<br />stock: IBM","theoretical:  0.707279786<br />sample:  0.8278915917<br />change:  8.278916e-01<br />stock: IBM","theoretical:  0.708676992<br />sample:  0.8314829346<br />change:  8.314829e-01<br />stock: IBM","theoretical:  0.710075583<br />sample:  0.8359857245<br />change:  8.359857e-01<br 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IBM","theoretical:  0.725553073<br />sample:  0.8577041057<br />change:  8.577041e-01<br />stock: IBM","theoretical:  0.726968718<br />sample:  0.8606105632<br />change:  8.606106e-01<br />stock: IBM","theoretical:  0.728385821<br />sample:  0.8616468065<br />change:  8.616468e-01<br />stock: IBM","theoretical:  0.729804389<br />sample:  0.8693362478<br />change:  8.693362e-01<br />stock: IBM","theoretical:  0.731224427<br />sample:  0.8716065238<br />change:  8.716065e-01<br />stock: IBM","theoretical:  0.732645941<br />sample:  0.8731153589<br />change:  8.731154e-01<br />stock: IBM","theoretical:  0.734068937<br />sample:  0.8736402700<br />change:  8.736403e-01<br />stock: IBM","theoretical:  0.735493421<br />sample:  0.8747372082<br />change:  8.747372e-01<br />stock: IBM","theoretical:  0.736919398<br />sample:  0.8757761675<br />change:  8.757762e-01<br />stock: IBM","theoretical:  0.738346876<br />sample:  0.8761631824<br />change:  8.761632e-01<br />stock: IBM","theoretical:  0.739775860<br />sample:  0.8783826797<br />change:  8.783827e-01<br />stock: IBM","theoretical:  0.741206357<br />sample:  0.8804092367<br />change:  8.804092e-01<br />stock: IBM","theoretical:  0.742638371<br />sample:  0.8804929753<br />change:  8.804930e-01<br />stock: IBM","theoretical:  0.744071911<br />sample:  0.8805727769<br />change:  8.805728e-01<br />stock: IBM","theoretical:  0.745506980<br />sample:  0.8814426875<br />change:  8.814427e-01<br />stock: IBM","theoretical:  0.746943587<br />sample:  0.8816657549<br />change:  8.816658e-01<br />stock: IBM","theoretical:  0.748381737<br />sample:  0.8830375399<br />change:  8.830375e-01<br />stock: IBM","theoretical:  0.749821437<br />sample:  0.8837321842<br />change:  8.837322e-01<br />stock: IBM","theoretical:  0.751262692<br />sample:  0.8877005624<br />change:  8.877006e-01<br />stock: IBM","theoretical:  0.752705510<br />sample:  0.8892718866<br />change:  8.892719e-01<br />stock: IBM","theoretical:  0.754149896<br />sample:  0.8897964763<br />change:  8.897965e-01<br />stock: IBM","theoretical:  0.755595858<br />sample:  0.8926593100<br />change:  8.926593e-01<br />stock: IBM","theoretical:  0.757043401<br />sample:  0.8935613320<br />change:  8.935613e-01<br />stock: IBM","theoretical:  0.758492532<br />sample:  0.8957563933<br />change:  8.957564e-01<br />stock: IBM","theoretical:  0.759943257<br />sample:  0.8971281927<br />change:  8.971282e-01<br />stock: IBM","theoretical:  0.761395584<br />sample:  0.9011785287<br />change:  9.011785e-01<br />stock: IBM","theoretical:  0.762849518<br />sample:  0.9013006721<br />change:  9.013007e-01<br />stock: IBM","theoretical:  0.764305067<br />sample:  0.9029965162<br />change:  9.029965e-01<br />stock: IBM","theoretical:  0.765762237<br />sample:  0.9060746361<br />change:  9.060746e-01<br />stock: IBM","theoretical:  0.767221035<br />sample:  0.9062002163<br />change:  9.062002e-01<br />stock: IBM","theoretical:  0.768681467<br />sample:  0.9069837620<br />change:  9.069838e-01<br />stock: IBM","theoretical:  0.770143541<br />sample:  0.9071784653<br />change:  9.071785e-01<br />stock: IBM","theoretical:  0.771607262<br />sample:  0.9087357676<br />change:  9.087358e-01<br />stock: IBM","theoretical:  0.773072639<br />sample:  0.9100536834<br />change:  9.100537e-01<br />stock: IBM","theoretical:  0.774539678<br />sample:  0.9124158625<br />change:  9.124159e-01<br />stock: IBM","theoretical:  0.776008386<br />sample:  0.9138383968<br />change:  9.138384e-01<br />stock: IBM","theoretical:  0.777478769<br />sample:  0.9140551541<br />change:  9.140552e-01<br />stock: IBM","theoretical:  0.778950835<br />sample:  0.9183830767<br />change:  9.183831e-01<br />stock: IBM","theoretical:  0.780424591<br />sample:  0.9203847149<br />change:  9.203847e-01<br />stock: IBM","theoretical:  0.781900044<br />sample:  0.9258280092<br />change:  9.258280e-01<br />stock: IBM","theoretical:  0.783377202<br />sample:  0.9264411644<br />change:  9.264412e-01<br />stock: IBM","theoretical:  0.784856070<br />sample:  0.9271973585<br />change:  9.271974e-01<br />stock: IBM","theoretical:  0.786336658<br />sample:  0.9289212802<br />change:  9.289213e-01<br />stock: IBM","theoretical:  0.787818970<br />sample:  0.9305402309<br />change:  9.305402e-01<br />stock: IBM","theoretical:  0.789303016<br />sample:  0.9322893991<br />change:  9.322894e-01<br />stock: IBM","theoretical:  0.790788803<br />sample:  0.9347750442<br />change:  9.347750e-01<br />stock: IBM","theoretical:  0.792276337<br />sample:  0.9357433924<br />change:  9.357434e-01<br />stock: IBM","theoretical:  0.793765626<br />sample:  0.9362152894<br />change:  9.362153e-01<br />stock: IBM","theoretical:  0.795256678<br />sample:  0.9362765052<br />change:  9.362765e-01<br />stock: IBM","theoretical:  0.796749500<br />sample:  0.9392265012<br />change:  9.392265e-01<br />stock: IBM","theoretical:  0.798244100<br />sample:  0.9392419757<br />change:  9.392420e-01<br />stock: IBM","theoretical:  0.799740485<br />sample:  0.9399943968<br />change:  9.399944e-01<br />stock: IBM","theoretical:  0.801238663<br />sample:  0.9408245916<br />change:  9.408246e-01<br />stock: IBM","theoretical:  0.802738641<br />sample:  0.9416268434<br />change:  9.416268e-01<br />stock: IBM","theoretical:  0.804240428<br />sample:  0.9499536071<br />change:  9.499536e-01<br />stock: IBM","theoretical:  0.805744031<br />sample:  0.9510171385<br />change:  9.510171e-01<br />stock: IBM","theoretical:  0.807249458<br />sample:  0.9511525007<br />change:  9.511525e-01<br />stock: IBM","theoretical:  0.808756716<br />sample:  0.9513108600<br />change:  9.513109e-01<br />stock: IBM","theoretical:  0.810265814<br />sample:  0.9517503010<br />change:  9.517503e-01<br />stock: IBM","theoretical:  0.811776760<br />sample:  0.9532386298<br />change:  9.532386e-01<br />stock: IBM","theoretical:  0.813289561<br />sample:  0.9535353406<br />change:  9.535353e-01<br />stock: IBM","theoretical:  0.814804226<br />sample:  0.9556876509<br />change:  9.556877e-01<br />stock: IBM","theoretical:  0.816320762<br />sample:  0.9573143957<br />change:  9.573144e-01<br />stock: IBM","theoretical:  0.817839178<br />sample:  0.9597662426<br />change:  9.597662e-01<br />stock: IBM","theoretical:  0.819359482<br />sample:  0.9629611429<br />change:  9.629611e-01<br />stock: IBM","theoretical:  0.820881682<br />sample:  0.9630789672<br />change:  9.630790e-01<br />stock: IBM","theoretical:  0.822405787<br />sample:  0.9683537847<br />change:  9.683538e-01<br />stock: IBM","theoretical:  0.823931804<br />sample:  0.9690835437<br />change:  9.690835e-01<br />stock: IBM","theoretical:  0.825459743<br />sample:  0.9699628046<br />change:  9.699628e-01<br />stock: IBM","theoretical:  0.826989611<br />sample:  0.9707903413<br />change:  9.707903e-01<br />stock: IBM","theoretical:  0.828521417<br />sample:  0.9712183556<br />change:  9.712184e-01<br />stock: IBM","theoretical:  0.830055169<br />sample:  0.9712561351<br />change:  9.712561e-01<br />stock: IBM","theoretical:  0.831590877<br />sample:  0.9713727341<br />change:  9.713727e-01<br />stock: IBM","theoretical:  0.833128549<br />sample:  0.9726086673<br />change:  9.726087e-01<br />stock: IBM","theoretical:  0.834668192<br />sample:  0.9760636880<br />change:  9.760637e-01<br />stock: IBM","theoretical:  0.836209817<br />sample:  0.9766833888<br />change:  9.766834e-01<br />stock: IBM","theoretical:  0.837753432<br />sample:  0.9773364090<br />change:  9.773364e-01<br />stock: IBM","theoretical:  0.839299046<br />sample:  0.9774379412<br />change:  9.774379e-01<br />stock: IBM","theoretical:  0.840846667<br />sample:  0.9789196840<br />change:  9.789197e-01<br />stock: IBM","theoretical:  0.842396305<br />sample:  0.9827152886<br />change:  9.827153e-01<br />stock: IBM","theoretical:  0.843947969<br />sample:  0.9873725571<br />change:  9.873726e-01<br />stock: IBM","theoretical:  0.845501667<br />sample:  0.9883543656<br />change:  9.883544e-01<br />stock: IBM","theoretical:  0.847057408<br />sample:  0.9893624485<br />change:  9.893624e-01<br />stock: IBM","theoretical:  0.848615203<br />sample:  0.9907656253<br />change:  9.907656e-01<br />stock: IBM","theoretical:  0.850175059<br />sample:  0.9909607213<br />change:  9.909607e-01<br />stock: IBM","theoretical:  0.851736987<br />sample:  0.9914503277<br />change:  9.914503e-01<br />stock: IBM","theoretical:  0.853300996<br />sample:  0.9919388558<br />change:  9.919389e-01<br />stock: IBM","theoretical:  0.854867095<br />sample:  0.9920828391<br />change:  9.920828e-01<br />stock: IBM","theoretical:  0.856435293<br />sample:  0.9936331503<br />change:  9.936332e-01<br />stock: IBM","theoretical:  0.858005600<br />sample:  0.9949466146<br />change:  9.949466e-01<br />stock: IBM","theoretical:  0.859578026<br />sample:  1.0010947536<br />change:  1.001095e+00<br />stock: IBM","theoretical:  0.861152580<br />sample:  1.0013599894<br />change:  1.001360e+00<br />stock: IBM","theoretical:  0.862729272<br />sample:  1.0034758313<br />change:  1.003476e+00<br />stock: IBM","theoretical:  0.864308112<br />sample:  1.0038864132<br />change:  1.003886e+00<br />stock: IBM","theoretical:  0.865889109<br />sample:  1.0048382205<br />change:  1.004838e+00<br />stock: IBM","theoretical:  0.867472273<br />sample:  1.0059672772<br />change:  1.005967e+00<br />stock: IBM","theoretical:  0.869057615<br />sample:  1.0078468603<br />change:  1.007847e+00<br />stock: IBM","theoretical:  0.870645144<br />sample:  1.0097203985<br />change:  1.009720e+00<br />stock: IBM","theoretical:  0.872234870<br />sample:  1.0106160648<br />change:  1.010616e+00<br />stock: IBM","theoretical:  0.873826803<br />sample:  1.0106913449<br />change:  1.010691e+00<br />stock: IBM","theoretical:  0.875420954<br />sample:  1.0122130673<br />change:  1.012213e+00<br />stock: IBM","theoretical:  0.877017333<br />sample:  1.0143628026<br />change:  1.014363e+00<br />stock: IBM","theoretical:  0.878615950<br />sample:  1.0173812101<br />change:  1.017381e+00<br />stock: IBM","theoretical:  0.880216816<br />sample:  1.0199862523<br />change:  1.019986e+00<br />stock: IBM","theoretical:  0.881819940<br />sample:  1.0264224578<br />change:  1.026422e+00<br />stock: IBM","theoretical:  0.883425335<br />sample:  1.0269662626<br />change:  1.026966e+00<br />stock: IBM","theoretical:  0.885033009<br />sample:  1.0273992244<br />change:  1.027399e+00<br />stock: IBM","theoretical:  0.886642974<br />sample:  1.0279733824<br />change:  1.027973e+00<br />stock: IBM","theoretical:  0.888255240<br />sample:  1.0314978445<br />change:  1.031498e+00<br />stock: IBM","theoretical:  0.889869818<br />sample:  1.0357030570<br />change:  1.035703e+00<br />stock: IBM","theoretical:  0.891486720<br />sample:  1.0357330800<br />change:  1.035733e+00<br />stock: IBM","theoretical:  0.893105956<br />sample:  1.0390432474<br />change:  1.039043e+00<br />stock: IBM","theoretical:  0.894727537<br />sample:  1.0395803733<br />change:  1.039580e+00<br />stock: IBM","theoretical:  0.896351473<br />sample:  1.0415021904<br />change:  1.041502e+00<br />stock: IBM","theoretical:  0.897977778<br />sample:  1.0416684501<br />change:  1.041668e+00<br />stock: IBM","theoretical:  0.899606460<br />sample:  1.0441391531<br />change:  1.044139e+00<br />stock: IBM","theoretical:  0.901237533<br />sample:  1.0442070808<br />change:  1.044207e+00<br />stock: IBM","theoretical:  0.902871006<br />sample:  1.0470859049<br />change:  1.047086e+00<br />stock: IBM","theoretical:  0.904506893<br />sample:  1.0474803136<br />change:  1.047480e+00<br />stock: IBM","theoretical:  0.906145203<br />sample:  1.0481511019<br />change:  1.048151e+00<br />stock: IBM","theoretical:  0.907785949<br />sample:  1.0508025587<br />change:  1.050803e+00<br />stock: IBM","theoretical:  0.909429143<br />sample:  1.0539145016<br />change:  1.053915e+00<br />stock: IBM","theoretical:  0.911074796<br />sample:  1.0540758575<br />change:  1.054076e+00<br />stock: IBM","theoretical:  0.912722920<br />sample:  1.0552779439<br />change:  1.055278e+00<br />stock: IBM","theoretical:  0.914373527<br />sample:  1.0558500573<br />change:  1.055850e+00<br />stock: IBM","theoretical:  0.916026629<br />sample:  1.0566743650<br />change:  1.056674e+00<br />stock: IBM","theoretical:  0.917682238<br />sample:  1.0577453667<br />change:  1.057745e+00<br />stock: IBM","theoretical:  0.919340366<br />sample:  1.0596898598<br />change:  1.059690e+00<br />stock: IBM","theoretical:  0.921001026<br />sample:  1.0621225030<br />change:  1.062123e+00<br />stock: IBM","theoretical:  0.922664229<br />sample:  1.0653972334<br />change:  1.065397e+00<br />stock: IBM","theoretical:  0.924329989<br />sample:  1.0661183352<br />change:  1.066118e+00<br />stock: IBM","theoretical:  0.925998317<br />sample:  1.0668645253<br />change:  1.066865e+00<br />stock: IBM","theoretical:  0.927669227<br />sample:  1.0673745317<br />change:  1.067375e+00<br />stock: IBM","theoretical:  0.929342731<br />sample:  1.0687654702<br />change:  1.068765e+00<br />stock: IBM","theoretical:  0.931018842<br />sample:  1.0691085989<br />change:  1.069109e+00<br />stock: IBM","theoretical:  0.932697572<br />sample:  1.0691887606<br />change:  1.069189e+00<br />stock: IBM","theoretical:  0.934378935<br />sample:  1.0699487968<br />change:  1.069949e+00<br />stock: IBM","theoretical:  0.936062943<br />sample:  1.0710870195<br />change:  1.071087e+00<br />stock: IBM","theoretical:  0.937749611<br />sample:  1.0711522112<br />change:  1.071152e+00<br />stock: IBM","theoretical:  0.939438950<br />sample:  1.0724734360<br />change:  1.072473e+00<br />stock: IBM","theoretical:  0.941130975<br />sample:  1.0744105225<br />change:  1.074411e+00<br />stock: IBM","theoretical:  0.942825698<br />sample:  1.0757354043<br />change:  1.075735e+00<br />stock: IBM","theoretical:  0.944523133<br />sample:  1.0861005586<br />change:  1.086101e+00<br />stock: IBM","theoretical:  0.946223295<br />sample:  1.0869521191<br />change:  1.086952e+00<br />stock: IBM","theoretical:  0.947926195<br />sample:  1.0880950463<br />change:  1.088095e+00<br />stock: IBM","theoretical:  0.949631850<br />sample:  1.0886137633<br />change:  1.088614e+00<br />stock: IBM","theoretical:  0.951340271<br />sample:  1.0912385853<br />change:  1.091239e+00<br />stock: IBM","theoretical:  0.953051473<br />sample:  1.0947104059<br />change:  1.094710e+00<br />stock: IBM","theoretical:  0.954765471<br />sample:  1.0948661765<br />change:  1.094866e+00<br />stock: IBM","theoretical:  0.956482279<br />sample:  1.0991562412<br />change:  1.099156e+00<br />stock: IBM","theoretical:  0.958201910<br />sample:  1.1004012698<br />change:  1.100401e+00<br />stock: IBM","theoretical:  0.959924379<br />sample:  1.1016555017<br />change:  1.101656e+00<br />stock: IBM","theoretical:  0.961649701<br />sample:  1.1031083580<br />change:  1.103108e+00<br />stock: IBM","theoretical:  0.963377890<br />sample:  1.1034466192<br />change:  1.103447e+00<br />stock: IBM","theoretical:  0.965108962<br />sample:  1.1039986465<br />change:  1.103999e+00<br />stock: IBM","theoretical:  0.966842930<br />sample:  1.1088422269<br />change:  1.108842e+00<br />stock: IBM","theoretical:  0.968579811<br />sample:  1.1090978023<br />change:  1.109098e+00<br />stock: IBM","theoretical:  0.970319618<br />sample:  1.1107932676<br />change:  1.110793e+00<br />stock: IBM","theoretical:  0.972062367<br />sample:  1.1116849988<br />change:  1.111685e+00<br />stock: IBM","theoretical:  0.973808073<br />sample:  1.1144678267<br />change:  1.114468e+00<br />stock: IBM","theoretical:  0.975556752<br />sample:  1.1157870131<br />change:  1.115787e+00<br />stock: IBM","theoretical:  0.977308420<br />sample:  1.1168346797<br />change:  1.116835e+00<br />stock: IBM","theoretical:  0.979063091<br />sample:  1.1179230912<br />change:  1.117923e+00<br />stock: IBM","theoretical:  0.980820782<br />sample:  1.1182349185<br />change:  1.118235e+00<br />stock: IBM","theoretical:  0.982581508<br />sample:  1.1185260702<br />change:  1.118526e+00<br />stock: IBM","theoretical:  0.984345286<br />sample:  1.1209750481<br />change:  1.120975e+00<br />stock: IBM","theoretical:  0.986112132<br />sample:  1.1236501642<br />change:  1.123650e+00<br />stock: IBM","theoretical:  0.987882061<br />sample:  1.1250469302<br />change:  1.125047e+00<br />stock: IBM","theoretical:  0.989655090<br />sample:  1.1275429028<br />change:  1.127543e+00<br />stock: IBM","theoretical:  0.991431236<br />sample:  1.1275742888<br />change:  1.127574e+00<br />stock: IBM","theoretical:  0.993210515<br />sample:  1.1325675774<br />change:  1.132568e+00<br />stock: IBM","theoretical:  0.994992944<br />sample:  1.1338704839<br />change:  1.133870e+00<br />stock: IBM","theoretical:  0.996778539<br />sample:  1.1372755289<br />change:  1.137276e+00<br />stock: IBM","theoretical:  0.998567319<br />sample:  1.1427774195<br />change:  1.142777e+00<br />stock: IBM","theoretical:  1.000359299<br />sample:  1.1441448812<br />change:  1.144145e+00<br />stock: IBM","theoretical:  1.002154497<br />sample:  1.1451555856<br />change:  1.145156e+00<br />stock: IBM","theoretical:  1.003952931<br />sample:  1.1482413799<br />change:  1.148241e+00<br />stock: IBM","theoretical:  1.005754618<br />sample:  1.1486509920<br />change:  1.148651e+00<br />stock: IBM","theoretical:  1.007559576<br />sample:  1.1545198286<br />change:  1.154520e+00<br />stock: IBM","theoretical:  1.009367822<br />sample:  1.1549175024<br />change:  1.154918e+00<br />stock: IBM","theoretical:  1.011179374<br />sample:  1.1555069007<br />change:  1.155507e+00<br />stock: IBM","theoretical:  1.012994251<br />sample:  1.1625393943<br />change:  1.162539e+00<br />stock: IBM","theoretical:  1.014812471<br />sample:  1.1673779105<br />change:  1.167378e+00<br />stock: IBM","theoretical:  1.016634052<br />sample:  1.1684264785<br />change:  1.168426e+00<br />stock: IBM","theoretical:  1.018459013<br />sample:  1.1715311691<br />change:  1.171531e+00<br />stock: IBM","theoretical:  1.020287371<br />sample:  1.1724840672<br />change:  1.172484e+00<br />stock: IBM","theoretical:  1.022119147<br />sample:  1.1739360283<br />change:  1.173936e+00<br />stock: IBM","theoretical:  1.023954359<br />sample:  1.1761003590<br />change:  1.176100e+00<br />stock: IBM","theoretical:  1.025793026<br />sample:  1.1784095163<br />change:  1.178410e+00<br />stock: IBM","theoretical:  1.027635168<br />sample:  1.1785636548<br />change:  1.178564e+00<br />stock: IBM","theoretical:  1.029480803<br />sample:  1.1830103869<br />change:  1.183010e+00<br />stock: IBM","theoretical:  1.031329952<br />sample:  1.1831152833<br />change:  1.183115e+00<br />stock: IBM","theoretical:  1.033182634<br />sample:  1.1832641481<br />change:  1.183264e+00<br />stock: IBM","theoretical:  1.035038869<br />sample:  1.1841126749<br />change:  1.184113e+00<br />stock: IBM","theoretical:  1.036898678<br />sample:  1.1859640335<br />change:  1.185964e+00<br />stock: IBM","theoretical:  1.038762080<br />sample:  1.1860836587<br />change:  1.186084e+00<br />stock: IBM","theoretical:  1.040629095<br />sample:  1.1886430363<br />change:  1.188643e+00<br />stock: IBM","theoretical:  1.042499746<br />sample:  1.1894162499<br />change:  1.189416e+00<br />stock: IBM","theoretical:  1.044374051<br />sample:  1.1902746595<br />change:  1.190275e+00<br />stock: IBM","theoretical:  1.046252032<br />sample:  1.1924466477<br />change:  1.192447e+00<br />stock: IBM","theoretical:  1.048133711<br />sample:  1.1926892022<br />change:  1.192689e+00<br />stock: IBM","theoretical:  1.050019108<br />sample:  1.1940269712<br />change:  1.194027e+00<br />stock: IBM","theoretical:  1.051908245<br />sample:  1.1970037160<br />change:  1.197004e+00<br />stock: IBM","theoretical:  1.053801144<br />sample:  1.2075082635<br />change:  1.207508e+00<br />stock: IBM","theoretical:  1.055697826<br />sample:  1.2155213760<br />change:  1.215521e+00<br />stock: IBM","theoretical:  1.057598314<br />sample:  1.2201266401<br />change:  1.220127e+00<br />stock: IBM","theoretical:  1.059502629<br />sample:  1.2206412898<br />change:  1.220641e+00<br />stock: IBM","theoretical:  1.061410794<br />sample:  1.2248259153<br />change:  1.224826e+00<br />stock: IBM","theoretical:  1.063322831<br />sample:  1.2276361986<br />change:  1.227636e+00<br />stock: IBM","theoretical:  1.065238764<br />sample:  1.2288739714<br />change:  1.228874e+00<br />stock: IBM","theoretical:  1.067158615<br />sample:  1.2289666114<br />change:  1.228967e+00<br />stock: IBM","theoretical:  1.069082408<br />sample:  1.2298399126<br />change:  1.229840e+00<br />stock: IBM","theoretical:  1.071010165<br />sample:  1.2357463845<br />change:  1.235746e+00<br />stock: IBM","theoretical:  1.072941911<br />sample:  1.2418825657<br />change:  1.241883e+00<br />stock: IBM","theoretical:  1.074877669<br />sample:  1.2475410649<br />change:  1.247541e+00<br />stock: IBM","theoretical:  1.076817463<br />sample:  1.2512284158<br />change:  1.251228e+00<br />stock: IBM","theoretical:  1.078761317<br />sample:  1.2539398501<br />change:  1.253940e+00<br />stock: IBM","theoretical:  1.080709257<br />sample:  1.2542575990<br />change:  1.254258e+00<br />stock: IBM","theoretical:  1.082661305<br />sample:  1.2547888521<br />change:  1.254789e+00<br />stock: IBM","theoretical:  1.084617488<br />sample:  1.2562130893<br />change:  1.256213e+00<br />stock: IBM","theoretical:  1.086577830<br />sample:  1.2580574694<br />change:  1.258057e+00<br />stock: IBM","theoretical:  1.088542357<br />sample:  1.2584122074<br />change:  1.258412e+00<br />stock: IBM","theoretical:  1.090511093<br />sample:  1.2620026393<br />change:  1.262003e+00<br />stock: IBM","theoretical:  1.092484066<br />sample:  1.2639665353<br />change:  1.263967e+00<br />stock: IBM","theoretical:  1.094461300<br />sample:  1.2642437317<br />change:  1.264244e+00<br />stock: IBM","theoretical:  1.096442823<br />sample:  1.2647194144<br />change:  1.264719e+00<br />stock: IBM","theoretical:  1.098428659<br />sample:  1.2657261120<br />change:  1.265726e+00<br />stock: IBM","theoretical:  1.100418837<br />sample:  1.2710391695<br />change:  1.271039e+00<br />stock: IBM","theoretical:  1.102413384<br />sample:  1.2734524989<br />change:  1.273452e+00<br />stock: IBM","theoretical:  1.104412325<br />sample:  1.2773400853<br />change:  1.277340e+00<br />stock: IBM","theoretical:  1.106415689<br />sample:  1.2801181940<br />change:  1.280118e+00<br />stock: IBM","theoretical:  1.108423504<br />sample:  1.2854568662<br />change:  1.285457e+00<br />stock: IBM","theoretical:  1.110435797<br />sample:  1.2871102915<br />change:  1.287110e+00<br />stock: IBM","theoretical:  1.112452597<br />sample:  1.2892605941<br />change:  1.289261e+00<br />stock: IBM","theoretical:  1.114473931<br />sample:  1.2899628709<br />change:  1.289963e+00<br />stock: IBM","theoretical:  1.116499830<br />sample:  1.2907693416<br />change:  1.290769e+00<br />stock: IBM","theoretical:  1.118530321<br />sample:  1.2945143780<br />change:  1.294514e+00<br />stock: IBM","theoretical:  1.120565435<br />sample:  1.2956282813<br />change:  1.295628e+00<br />stock: IBM","theoretical:  1.122605200<br />sample:  1.2996717151<br />change:  1.299672e+00<br />stock: IBM","theoretical:  1.124649646<br />sample:  1.3085583402<br />change:  1.308558e+00<br />stock: IBM","theoretical:  1.126698804<br />sample:  1.3093784133<br />change:  1.309378e+00<br />stock: IBM","theoretical:  1.128752704<br />sample:  1.3099773499<br />change:  1.309977e+00<br />stock: IBM","theoretical:  1.130811377<br />sample:  1.3129809879<br />change:  1.312981e+00<br />stock: IBM","theoretical:  1.132874854<br />sample:  1.3153206394<br />change:  1.315321e+00<br />stock: IBM","theoretical:  1.134943166<br />sample:  1.3160746793<br />change:  1.316075e+00<br />stock: IBM","theoretical:  1.137016344<br />sample:  1.3167601003<br />change:  1.316760e+00<br />stock: IBM","theoretical:  1.139094421<br />sample:  1.3181799547<br />change:  1.318180e+00<br />stock: IBM","theoretical:  1.141177428<br />sample:  1.3217896534<br />change:  1.321790e+00<br />stock: IBM","theoretical:  1.143265399<br />sample:  1.3220460386<br />change:  1.322046e+00<br />stock: IBM","theoretical:  1.145358366<br />sample:  1.3265270994<br />change:  1.326527e+00<br />stock: IBM","theoretical:  1.147456362<br />sample:  1.3287444834<br />change:  1.328744e+00<br />stock: IBM","theoretical:  1.149559421<br />sample:  1.3301704095<br />change:  1.330170e+00<br />stock: IBM","theoretical:  1.151667577<br />sample:  1.3324436160<br />change:  1.332444e+00<br />stock: IBM","theoretical:  1.153780863<br />sample:  1.3326108370<br />change:  1.332611e+00<br />stock: IBM","theoretical:  1.155899315<br />sample:  1.3340990443<br />change:  1.334099e+00<br />stock: IBM","theoretical:  1.158022968<br />sample:  1.3361162742<br />change:  1.336116e+00<br />stock: IBM","theoretical:  1.160151855<br />sample:  1.3371656450<br />change:  1.337166e+00<br />stock: IBM","theoretical:  1.162286014<br />sample:  1.3385106445<br />change:  1.338511e+00<br />stock: IBM","theoretical:  1.164425479<br />sample:  1.3468339602<br />change:  1.346834e+00<br />stock: IBM","theoretical:  1.166570288<br />sample:  1.3525549578<br />change:  1.352555e+00<br />stock: IBM","theoretical:  1.168720477<br />sample:  1.3564584649<br />change:  1.356458e+00<br />stock: IBM","theoretical:  1.170876083<br />sample:  1.3632284130<br />change:  1.363228e+00<br />stock: IBM","theoretical:  1.173037143<br />sample:  1.3658017394<br />change:  1.365802e+00<br />stock: IBM","theoretical:  1.175203696<br />sample:  1.3674757113<br />change:  1.367476e+00<br />stock: IBM","theoretical:  1.177375778<br />sample:  1.3683513198<br />change:  1.368351e+00<br />stock: IBM","theoretical:  1.179553430<br />sample:  1.3746734462<br />change:  1.374673e+00<br />stock: IBM","theoretical:  1.181736690<br />sample:  1.3792461420<br />change:  1.379246e+00<br />stock: IBM","theoretical:  1.183925598<br />sample:  1.3819203236<br />change:  1.381920e+00<br />stock: IBM","theoretical:  1.186120192<br />sample:  1.3825547261<br />change:  1.382555e+00<br />stock: IBM","theoretical:  1.188320515<br />sample:  1.3830844153<br />change:  1.383084e+00<br />stock: IBM","theoretical:  1.190526605<br />sample:  1.3833109637<br />change:  1.383311e+00<br />stock: IBM","theoretical:  1.192738505<br />sample:  1.3886152993<br />change:  1.388615e+00<br />stock: IBM","theoretical:  1.194956256<br />sample:  1.3893023167<br />change:  1.389302e+00<br />stock: IBM","theoretical:  1.197179900<br />sample:  1.3894591928<br />change:  1.389459e+00<br />stock: IBM","theoretical:  1.199409479<br />sample:  1.3905454215<br />change:  1.390545e+00<br />stock: IBM","theoretical:  1.201645037<br />sample:  1.3916170267<br />change:  1.391617e+00<br />stock: IBM","theoretical:  1.203886616<br />sample:  1.4044918919<br />change:  1.404492e+00<br />stock: IBM","theoretical:  1.206134260<br />sample:  1.4066972638<br />change:  1.406697e+00<br />stock: IBM","theoretical:  1.208388015<br />sample:  1.4152143085<br />change:  1.415214e+00<br />stock: IBM","theoretical:  1.210647924<br />sample:  1.4171448772<br />change:  1.417145e+00<br />stock: IBM","theoretical:  1.212914033<br />sample:  1.4238105206<br />change:  1.423811e+00<br />stock: IBM","theoretical:  1.215186388<br />sample:  1.4258439469<br />change:  1.425844e+00<br />stock: IBM","theoretical:  1.217465035<br />sample:  1.4292308872<br />change:  1.429231e+00<br />stock: IBM","theoretical:  1.219750021<br />sample:  1.4321796241<br />change:  1.432180e+00<br />stock: IBM","theoretical:  1.222041393<br />sample:  1.4340095979<br />change:  1.434010e+00<br />stock: IBM","theoretical:  1.224339200<br />sample:  1.4348746892<br />change:  1.434875e+00<br />stock: IBM","theoretical:  1.226643489<br />sample:  1.4451834422<br />change:  1.445183e+00<br />stock: IBM","theoretical:  1.228954310<br />sample:  1.4478598597<br />change:  1.447860e+00<br />stock: IBM","theoretical:  1.231271712<br />sample:  1.4547926321<br />change:  1.454793e+00<br />stock: IBM","theoretical:  1.233595745<br />sample:  1.4555305309<br />change:  1.455531e+00<br />stock: IBM","theoretical:  1.235926461<br />sample:  1.4557746542<br />change:  1.455775e+00<br />stock: IBM","theoretical:  1.238263909<br />sample:  1.4591262929<br />change:  1.459126e+00<br />stock: IBM","theoretical:  1.240608143<br />sample:  1.4631792222<br />change:  1.463179e+00<br />stock: IBM","theoretical:  1.242959214<br />sample:  1.4656152464<br />change:  1.465615e+00<br />stock: IBM","theoretical:  1.245317176<br />sample:  1.4693967222<br />change:  1.469397e+00<br />stock: IBM","theoretical:  1.247682083<br />sample:  1.4770723979<br />change:  1.477072e+00<br />stock: IBM","theoretical:  1.250053987<br />sample:  1.4848997107<br />change:  1.484900e+00<br />stock: IBM","theoretical:  1.252432946<br />sample:  1.4876706139<br />change:  1.487671e+00<br />stock: IBM","theoretical:  1.254819014<br />sample:  1.4879021668<br />change:  1.487902e+00<br />stock: IBM","theoretical:  1.257212247<br />sample:  1.4886875310<br />change:  1.488688e+00<br />stock: IBM","theoretical:  1.259612703<br />sample:  1.4898360922<br />change:  1.489836e+00<br />stock: IBM","theoretical:  1.262020439<br />sample:  1.4922890673<br />change:  1.492289e+00<br />stock: IBM","theoretical:  1.264435514<br />sample:  1.4945443929<br />change:  1.494544e+00<br />stock: IBM","theoretical:  1.266857986<br />sample:  1.4950957085<br />change:  1.495096e+00<br />stock: IBM","theoretical:  1.269287916<br />sample:  1.5019860673<br />change:  1.501986e+00<br />stock: IBM","theoretical:  1.271725363<br />sample:  1.5057490057<br />change:  1.505749e+00<br />stock: IBM","theoretical:  1.274170389<br />sample:  1.5074287297<br />change:  1.507429e+00<br />stock: IBM","theoretical:  1.276623056<br />sample:  1.5103745658<br />change:  1.510375e+00<br />stock: IBM","theoretical:  1.279083427<br />sample:  1.5187662143<br />change:  1.518766e+00<br />stock: IBM","theoretical:  1.281551566<br />sample:  1.5191997225<br />change:  1.519200e+00<br />stock: IBM","theoretical:  1.284027535<br />sample:  1.5447915841<br />change:  1.544792e+00<br />stock: IBM","theoretical:  1.286511402<br />sample:  1.5554834433<br />change:  1.555483e+00<br />stock: IBM","theoretical:  1.289003232<br />sample:  1.5702039550<br />change:  1.570204e+00<br />stock: IBM","theoretical:  1.291503090<br />sample:  1.5761789072<br />change:  1.576179e+00<br />stock: IBM","theoretical:  1.294011047<br />sample:  1.5769183117<br />change:  1.576918e+00<br />stock: IBM","theoretical:  1.296527168<br />sample:  1.5773657768<br />change:  1.577366e+00<br />stock: IBM","theoretical:  1.299051525<br />sample:  1.5867063269<br />change:  1.586706e+00<br />stock: IBM","theoretical:  1.301584187<br />sample:  1.5882105784<br />change:  1.588211e+00<br />stock: IBM","theoretical:  1.304125225<br />sample:  1.5948431027<br />change:  1.594843e+00<br />stock: IBM","theoretical:  1.306674713<br />sample:  1.5971758278<br />change:  1.597176e+00<br />stock: IBM","theoretical:  1.309232721<br />sample:  1.6018892212<br />change:  1.601889e+00<br />stock: IBM","theoretical:  1.311799326<br />sample:  1.6056443292<br />change:  1.605644e+00<br />stock: IBM","theoretical:  1.314374601<br />sample:  1.6061022422<br />change:  1.606102e+00<br />stock: IBM","theoretical:  1.316958622<br />sample:  1.6165225263<br />change:  1.616523e+00<br />stock: IBM","theoretical:  1.319551468<br />sample:  1.6376770914<br />change:  1.637677e+00<br />stock: IBM","theoretical:  1.322153215<br />sample:  1.6396180281<br />change:  1.639618e+00<br />stock: IBM","theoretical:  1.324763942<br />sample:  1.6610672304<br />change:  1.661067e+00<br />stock: IBM","theoretical:  1.327383731<br />sample:  1.6612754268<br />change:  1.661275e+00<br />stock: IBM","theoretical:  1.330012661<br />sample:  1.6613588298<br />change:  1.661359e+00<br />stock: IBM","theoretical:  1.332650816<br />sample:  1.6626715458<br />change:  1.662672e+00<br />stock: IBM","theoretical:  1.335298278<br />sample:  1.6727369424<br />change:  1.672737e+00<br />stock: IBM","theoretical:  1.337955133<br />sample:  1.6816503984<br />change:  1.681650e+00<br />stock: IBM","theoretical:  1.340621467<br />sample:  1.6874394700<br />change:  1.687439e+00<br />stock: IBM","theoretical:  1.343297365<br />sample:  1.6976629545<br />change:  1.697663e+00<br />stock: IBM","theoretical:  1.345982917<br />sample:  1.6977834607<br />change:  1.697783e+00<br />stock: IBM","theoretical:  1.348678211<br />sample:  1.7022342471<br />change:  1.702234e+00<br />stock: IBM","theoretical:  1.351383339<br />sample:  1.7028594368<br />change:  1.702859e+00<br />stock: IBM","theoretical:  1.354098392<br />sample:  1.7041326662<br />change:  1.704133e+00<br />stock: IBM","theoretical:  1.356823464<br />sample:  1.7049847706<br />change:  1.704985e+00<br />stock: IBM","theoretical:  1.359558649<br />sample:  1.7099018859<br />change:  1.709902e+00<br />stock: IBM","theoretical:  1.362304043<br />sample:  1.7205304754<br />change:  1.720530e+00<br />stock: IBM","theoretical:  1.365059744<br />sample:  1.7213346943<br />change:  1.721335e+00<br />stock: IBM","theoretical:  1.367825850<br />sample:  1.7249127111<br />change:  1.724913e+00<br />stock: IBM","theoretical:  1.370602461<br />sample:  1.7270246087<br />change:  1.727025e+00<br />stock: IBM","theoretical:  1.373389680<br />sample:  1.7331504533<br />change:  1.733150e+00<br />stock: IBM","theoretical:  1.376187608<br />sample:  1.7429262992<br />change:  1.742926e+00<br />stock: IBM","theoretical:  1.378996352<br />sample:  1.7436331802<br />change:  1.743633e+00<br />stock: IBM","theoretical:  1.381816018<br />sample:  1.7523982450<br />change:  1.752398e+00<br />stock: IBM","theoretical:  1.384646712<br />sample:  1.7525410779<br />change:  1.752541e+00<br />stock: IBM","theoretical:  1.387488545<br />sample:  1.7547559058<br />change:  1.754756e+00<br />stock: IBM","theoretical:  1.390341628<br />sample:  1.7562101243<br />change:  1.756210e+00<br />stock: IBM","theoretical:  1.393206073<br />sample:  1.7636548623<br />change:  1.763655e+00<br />stock: IBM","theoretical:  1.396081996<br />sample:  1.7681840763<br />change:  1.768184e+00<br />stock: IBM","theoretical:  1.398969512<br />sample:  1.7741474945<br />change:  1.774147e+00<br />stock: IBM","theoretical:  1.401868740<br />sample:  1.7818882188<br />change:  1.781888e+00<br />stock: IBM","theoretical:  1.404779799<br />sample:  1.7850039622<br />change:  1.785004e+00<br />stock: IBM","theoretical:  1.407702812<br />sample:  1.7874699803<br />change:  1.787470e+00<br />stock: IBM","theoretical:  1.410637901<br />sample:  1.7902576875<br />change:  1.790258e+00<br />stock: IBM","theoretical:  1.413585194<br />sample:  1.7908636965<br />change:  1.790864e+00<br />stock: IBM","theoretical:  1.416544817<br />sample:  1.7933521490<br />change:  1.793352e+00<br />stock: IBM","theoretical:  1.419516901<br />sample:  1.8041713280<br />change:  1.804171e+00<br />stock: IBM","theoretical:  1.422501577<br />sample:  1.8107907392<br />change:  1.810791e+00<br />stock: IBM","theoretical:  1.425498978<br />sample:  1.8148841068<br />change:  1.814884e+00<br />stock: IBM","theoretical:  1.428509243<br />sample:  1.8157429136<br />change:  1.815743e+00<br />stock: IBM","theoretical:  1.431532507<br />sample:  1.8172959181<br />change:  1.817296e+00<br />stock: IBM","theoretical:  1.434568914<br />sample:  1.8185019910<br />change:  1.818502e+00<br />stock: IBM","theoretical:  1.437618604<br />sample:  1.8240666431<br />change:  1.824067e+00<br />stock: IBM","theoretical:  1.440681724<br />sample:  1.8241165362<br />change:  1.824117e+00<br />stock: IBM","theoretical:  1.443758422<br />sample:  1.8320389222<br />change:  1.832039e+00<br />stock: IBM","theoretical:  1.446848847<br />sample:  1.8337130636<br />change:  1.833713e+00<br />stock: IBM","theoretical:  1.449953153<br />sample:  1.8338895787<br />change:  1.833890e+00<br />stock: IBM","theoretical:  1.453071495<br />sample:  1.8368516474<br />change:  1.836852e+00<br />stock: IBM","theoretical:  1.456204031<br />sample:  1.8377580251<br />change:  1.837758e+00<br />stock: IBM","theoretical:  1.459350922<br />sample:  1.8380073174<br />change:  1.838007e+00<br />stock: IBM","theoretical:  1.462512331<br />sample:  1.8392313666<br />change:  1.839231e+00<br />stock: IBM","theoretical:  1.465688426<br />sample:  1.8424743199<br />change:  1.842474e+00<br />stock: IBM","theoretical:  1.468879375<br />sample:  1.8484690958<br />change:  1.848469e+00<br />stock: IBM","theoretical:  1.472085351<br />sample:  1.8509701083<br />change:  1.850970e+00<br />stock: IBM","theoretical:  1.475306529<br />sample:  1.8526658635<br />change:  1.852666e+00<br />stock: IBM","theoretical:  1.478543088<br />sample:  1.8531195427<br />change:  1.853120e+00<br />stock: IBM","theoretical:  1.481795210<br />sample:  1.8570880243<br />change:  1.857088e+00<br />stock: IBM","theoretical:  1.485063080<br />sample:  1.8599067946<br />change:  1.859907e+00<br />stock: IBM","theoretical:  1.488346886<br />sample:  1.8628968003<br />change:  1.862897e+00<br />stock: IBM","theoretical:  1.491646821<br />sample:  1.8684491462<br />change:  1.868449e+00<br />stock: IBM","theoretical:  1.494963079<br />sample:  1.8719479714<br />change:  1.871948e+00<br />stock: IBM","theoretical:  1.498295860<br />sample:  1.8919683042<br />change:  1.891968e+00<br />stock: IBM","theoretical:  1.501645367<br />sample:  1.9027118552<br />change:  1.902712e+00<br />stock: IBM","theoretical:  1.505011807<br />sample:  1.9057100542<br />change:  1.905710e+00<br />stock: IBM","theoretical:  1.508395390<br />sample:  1.9162611730<br />change:  1.916261e+00<br />stock: IBM","theoretical:  1.511796330<br />sample:  1.9210359710<br />change:  1.921036e+00<br />stock: IBM","theoretical:  1.515214847<br />sample:  1.9291307126<br />change:  1.929131e+00<br />stock: IBM","theoretical:  1.518651164<br />sample:  1.9555803727<br />change:  1.955580e+00<br />stock: IBM","theoretical:  1.522105507<br />sample:  1.9588449835<br />change:  1.958845e+00<br />stock: IBM","theoretical:  1.525578109<br />sample:  1.9596683039<br />change:  1.959668e+00<br />stock: IBM","theoretical:  1.529069205<br />sample:  1.9654264697<br />change:  1.965426e+00<br />stock: IBM","theoretical:  1.532579038<br />sample:  1.9665068061<br />change:  1.966507e+00<br />stock: IBM","theoretical:  1.536107853<br />sample:  1.9757372970<br />change:  1.975737e+00<br />stock: IBM","theoretical:  1.539655901<br />sample:  1.9858643066<br />change:  1.985864e+00<br />stock: IBM","theoretical:  1.543223437<br />sample:  1.9910000429<br />change:  1.991000e+00<br />stock: IBM","theoretical:  1.546810723<br />sample:  1.9946268339<br />change:  1.994627e+00<br />stock: IBM","theoretical:  1.550418026<br />sample:  2.0085745043<br />change:  2.008575e+00<br />stock: IBM","theoretical:  1.554045617<br />sample:  2.0104189107<br />change:  2.010419e+00<br />stock: IBM","theoretical:  1.557693775<br />sample:  2.0124577268<br />change:  2.012458e+00<br />stock: IBM","theoretical:  1.561362783<br />sample:  2.0263827135<br />change:  2.026383e+00<br />stock: IBM","theoretical:  1.565052930<br />sample:  2.0305103298<br />change:  2.030510e+00<br />stock: IBM","theoretical:  1.568764514<br />sample:  2.0313504253<br />change:  2.031350e+00<br />stock: IBM","theoretical:  1.572497834<br />sample:  2.0325552962<br />change:  2.032555e+00<br />stock: IBM","theoretical:  1.576253202<br />sample:  2.0502306738<br />change:  2.050231e+00<br />stock: IBM","theoretical:  1.580030931<br />sample:  2.0531568985<br />change:  2.053157e+00<br />stock: IBM","theoretical:  1.583831345<br />sample:  2.0574649766<br />change:  2.057465e+00<br />stock: IBM","theoretical:  1.587654774<br />sample:  2.0600341282<br />change:  2.060034e+00<br />stock: IBM","theoretical:  1.591501553<br />sample:  2.0695451427<br />change:  2.069545e+00<br />stock: IBM","theoretical:  1.595372028<br />sample:  2.0729223258<br />change:  2.072922e+00<br />stock: IBM","theoretical:  1.599266552<br />sample:  2.0816309984<br />change:  2.081631e+00<br />stock: IBM","theoretical:  1.603185484<br />sample:  2.0853931606<br />change:  2.085393e+00<br />stock: IBM","theoretical:  1.607129194<br />sample:  2.0930869323<br />change:  2.093087e+00<br />stock: IBM","theoretical:  1.611098059<br />sample:  2.1027653287<br />change:  2.102765e+00<br />stock: IBM","theoretical:  1.615092465<br />sample:  2.1426395883<br />change:  2.142640e+00<br />stock: IBM","theoretical:  1.619112808<br />sample:  2.1440743873<br />change:  2.144074e+00<br />stock: IBM","theoretical:  1.623159493<br />sample:  2.1487081025<br />change:  2.148708e+00<br />stock: IBM","theoretical:  1.627232934<br />sample:  2.1500159716<br />change:  2.150016e+00<br />stock: IBM","theoretical:  1.631333556<br />sample:  2.1543606567<br />change:  2.154361e+00<br />stock: IBM","theoretical:  1.635461794<br />sample:  2.1665148364<br />change:  2.166515e+00<br />stock: IBM","theoretical:  1.639618093<br />sample:  2.1675259977<br />change:  2.167526e+00<br />stock: IBM","theoretical:  1.643802912<br />sample:  2.1697700619<br />change:  2.169770e+00<br />stock: IBM","theoretical:  1.648016717<br />sample:  2.1734890516<br />change:  2.173489e+00<br />stock: IBM","theoretical:  1.652259990<br />sample:  2.1752435775<br />change:  2.175244e+00<br />stock: IBM","theoretical:  1.656533223<br />sample:  2.1839121051<br />change:  2.183912e+00<br />stock: IBM","theoretical:  1.660836920<br />sample:  2.1841691083<br />change:  2.184169e+00<br />stock: IBM","theoretical:  1.665171601<br />sample:  2.1972084534<br />change:  2.197208e+00<br />stock: IBM","theoretical:  1.669537798<br />sample:  2.1979811819<br />change:  2.197981e+00<br />stock: IBM","theoretical:  1.673936056<br />sample:  2.2060645699<br />change:  2.206065e+00<br />stock: IBM","theoretical:  1.678366937<br />sample:  2.2240310007<br />change:  2.224031e+00<br />stock: IBM","theoretical:  1.682831015<br />sample:  2.2495023129<br />change:  2.249502e+00<br />stock: IBM","theoretical:  1.687328883<br />sample:  2.2749782755<br />change:  2.274978e+00<br />stock: IBM","theoretical:  1.691861149<br />sample:  2.2946434722<br />change:  2.294643e+00<br />stock: IBM","theoretical:  1.696428436<br />sample:  2.3089683897<br />change:  2.308968e+00<br />stock: IBM","theoretical:  1.701031388<br />sample:  2.3192034636<br />change:  2.319203e+00<br />stock: IBM","theoretical:  1.705670665<br />sample:  2.3312810532<br />change:  2.331281e+00<br />stock: IBM","theoretical:  1.710346946<br />sample:  2.3332651095<br />change:  2.333265e+00<br />stock: IBM","theoretical:  1.715060931<br />sample:  2.3492622012<br />change:  2.349262e+00<br />stock: IBM","theoretical:  1.719813337<br />sample:  2.3578059898<br />change:  2.357806e+00<br />stock: IBM","theoretical:  1.724604907<br />sample:  2.3784818720<br />change:  2.378482e+00<br />stock: IBM","theoretical:  1.729436403<br />sample:  2.4060661565<br />change:  2.406066e+00<br />stock: IBM","theoretical:  1.734308610<br />sample:  2.4109392427<br />change:  2.410939e+00<br />stock: IBM","theoretical:  1.739222339<br />sample:  2.4565054795<br />change:  2.456505e+00<br />stock: IBM","theoretical:  1.744178422<br />sample:  2.4634663052<br />change:  2.463466e+00<br />stock: IBM","theoretical:  1.749177722<br />sample:  2.4690428738<br />change:  2.469043e+00<br />stock: IBM","theoretical:  1.754221125<br />sample:  2.4708893700<br />change:  2.470889e+00<br />stock: IBM","theoretical:  1.759309548<br />sample:  2.4710888430<br />change:  2.471089e+00<br />stock: IBM","theoretical:  1.764443934<br />sample:  2.4751193563<br />change:  2.475119e+00<br />stock: IBM","theoretical:  1.769625261<br />sample:  2.4908633695<br />change:  2.490863e+00<br />stock: IBM","theoretical:  1.774854535<br />sample:  2.5047680758<br />change:  2.504768e+00<br />stock: IBM","theoretical:  1.780132799<br />sample:  2.5058745919<br />change:  2.505875e+00<br />stock: IBM","theoretical:  1.785461129<br />sample:  2.5074085670<br />change:  2.507409e+00<br />stock: IBM","theoretical:  1.790840637<br />sample:  2.5120799758<br />change:  2.512080e+00<br />stock: IBM","theoretical:  1.796272476<br />sample:  2.5140586062<br />change:  2.514059e+00<br />stock: IBM","theoretical:  1.801757836<br />sample:  2.5317171735<br />change:  2.531717e+00<br />stock: IBM","theoretical:  1.807297952<br />sample:  2.5448688627<br />change:  2.544869e+00<br />stock: IBM","theoretical:  1.812894101<br />sample:  2.5490315390<br />change:  2.549032e+00<br />stock: IBM","theoretical:  1.818547608<br />sample:  2.5643073626<br />change:  2.564307e+00<br />stock: IBM","theoretical:  1.824259843<br />sample:  2.5778285040<br />change:  2.577829e+00<br />stock: IBM","theoretical:  1.830032232<br />sample:  2.5889965771<br />change:  2.588997e+00<br />stock: IBM","theoretical:  1.835866250<br />sample:  2.5931986032<br />change:  2.593199e+00<br />stock: IBM","theoretical:  1.841763431<br />sample:  2.6077876886<br />change:  2.607788e+00<br />stock: IBM","theoretical:  1.847725366<br />sample:  2.6100176396<br />change:  2.610018e+00<br />stock: IBM","theoretical:  1.853753712<br />sample:  2.6410774949<br />change:  2.641077e+00<br />stock: IBM","theoretical:  1.859850187<br />sample:  2.6559514790<br />change:  2.655951e+00<br />stock: IBM","theoretical:  1.866016582<br />sample:  2.6636121397<br />change:  2.663612e+00<br />stock: IBM","theoretical:  1.872254759<br />sample:  2.6895905109<br />change:  2.689591e+00<br />stock: IBM","theoretical:  1.878566656<br />sample:  2.7068333086<br />change:  2.706833e+00<br />stock: IBM","theoretical:  1.884954295<br />sample:  2.7142842627<br />change:  2.714284e+00<br />stock: IBM","theoretical:  1.891419784<br />sample:  2.7367803372<br />change:  2.736780e+00<br />stock: IBM","theoretical:  1.897965319<br />sample:  2.7374939341<br />change:  2.737494e+00<br />stock: IBM","theoretical:  1.904593195<br />sample:  2.7670352381<br />change:  2.767035e+00<br />stock: IBM","theoretical:  1.911305810<br />sample:  2.7758630776<br />change:  2.775863e+00<br />stock: IBM","theoretical:  1.918105668<br />sample:  2.8024505893<br />change:  2.802451e+00<br />stock: IBM","theoretical:  1.924995390<br />sample:  2.8043594393<br />change:  2.804359e+00<br />stock: IBM","theoretical:  1.931977719<br />sample:  2.8164228268<br />change:  2.816423e+00<br />stock: IBM","theoretical:  1.939055529<br />sample:  2.8231355433<br />change:  2.823136e+00<br />stock: IBM","theoretical:  1.946231830<br />sample:  2.8307727273<br />change:  2.830773e+00<br />stock: IBM","theoretical:  1.953509784<br />sample:  2.8478051118<br />change:  2.847805e+00<br />stock: IBM","theoretical:  1.960892708<br />sample:  2.8673265750<br />change:  2.867327e+00<br />stock: IBM","theoretical:  1.968384089<br />sample:  2.9086238438<br />change:  2.908624e+00<br />stock: IBM","theoretical:  1.975987595<br />sample:  2.9224554230<br />change:  2.922455e+00<br />stock: IBM","theoretical:  1.983707085<br />sample:  2.9511397548<br />change:  2.951140e+00<br />stock: IBM","theoretical:  1.991546628<br />sample:  2.9765312233<br />change:  2.976531e+00<br />stock: IBM","theoretical:  1.999510515<br />sample:  3.0155364922<br />change:  3.015536e+00<br />stock: IBM","theoretical:  2.007603274<br />sample:  3.0508461356<br />change:  3.050846e+00<br />stock: IBM","theoretical:  2.015829694<br />sample:  3.0530282559<br />change:  3.053028e+00<br />stock: IBM","theoretical:  2.024194838<br />sample:  3.0719382603<br />change:  3.071938e+00<br />stock: IBM","theoretical:  2.032704074<br />sample:  3.0847916108<br />change:  3.084792e+00<br />stock: IBM","theoretical:  2.041363088<br />sample:  3.1341245366<br />change:  3.134125e+00<br />stock: IBM","theoretical:  2.050177922<br />sample:  3.1666164976<br />change:  3.166616e+00<br />stock: IBM","theoretical:  2.059154998<br />sample:  3.1897015127<br />change:  3.189702e+00<br />stock: IBM","theoretical:  2.068301150<br />sample:  3.2400928856<br />change:  3.240093e+00<br />stock: IBM","theoretical:  2.077623666<br />sample:  3.2744259079<br />change:  3.274426e+00<br />stock: IBM","theoretical:  2.087130323<br />sample:  3.2885959580<br />change:  3.288596e+00<br />stock: IBM","theoretical:  2.096829437<br />sample:  3.3455087803<br />change:  3.345509e+00<br />stock: IBM","theoretical:  2.106729912<br />sample:  3.3557025175<br />change:  3.355703e+00<br />stock: IBM","theoretical:  2.116841300<br />sample:  3.3589203415<br />change:  3.358920e+00<br />stock: IBM","theoretical:  2.127173863<br />sample:  3.4094210481<br />change:  3.409421e+00<br />stock: IBM","theoretical:  2.137738647<br />sample:  3.4152323376<br />change:  3.415232e+00<br />stock: IBM","theoretical:  2.148547566<br />sample:  3.4169449828<br />change:  3.416945e+00<br />stock: IBM","theoretical:  2.159613493<br />sample:  3.4393590710<br />change:  3.439359e+00<br />stock: IBM","theoretical:  2.170950371<br />sample:  3.4450150815<br />change:  3.445015e+00<br />stock: IBM","theoretical:  2.182573337<br />sample:  3.4475191538<br />change:  3.447519e+00<br />stock: IBM","theoretical:  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Compared to Density Plot

This is another way of comparing the different stocks: this density plot also shows that outlier values are most common for Starbucks and Apple.

library(plotly)
stocks <- read.csv("https://raw.githubusercontent.com/plotly/datasets/master/stockdata2.csv",
                   stringsAsFactors = FALSE)

p <- ggplot(stocks, aes(x=change)) +
  geom_density(aes(color=stock))

ggplotly(p)

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Facetted

library(plotly)
stocks <- read.csv("https://raw.githubusercontent.com/plotly/datasets/master/stockdata2.csv",
                   stringsAsFactors = FALSE)

p <- ggplot(stocks, aes(sample=change))+
  geom_qq_line() + geom_qq(aes(colour=stock), alpha=0.3, size=0.1) +
  facet_wrap(~stock) +
  ylim(-10,10)

ggplotly(p)

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0.0320542132<br />change:  3.205421e-02<br />stock: IBM","theoretical:  0.005437398<br />sample:  0.0329038345<br />change:  3.290383e-02<br />stock: IBM","theoretical:  0.006524892<br />sample:  0.0342974562<br />change:  3.429746e-02<br />stock: IBM","theoretical:  0.007612394<br />sample:  0.0389279432<br />change:  3.892794e-02<br />stock: IBM","theoretical:  0.008699904<br />sample:  0.0451166774<br />change:  4.511668e-02<br />stock: IBM","theoretical:  0.009787425<br />sample:  0.0467513366<br />change:  4.675134e-02<br />stock: IBM","theoretical:  0.010874957<br />sample:  0.0492506773<br />change:  4.925068e-02<br />stock: IBM","theoretical:  0.011962503<br />sample:  0.0510600862<br />change:  5.106009e-02<br />stock: IBM","theoretical:  0.013050062<br />sample:  0.0519515368<br />change:  5.195154e-02<br />stock: IBM","theoretical:  0.014137637<br />sample:  0.0521920119<br />change:  5.219201e-02<br />stock: IBM","theoretical:  0.015225228<br />sample:  0.0530938373<br />change:  5.309384e-02<br />stock: IBM","theoretical:  0.016312838<br />sample:  0.0533310197<br />change:  5.333102e-02<br />stock: IBM","theoretical:  0.017400467<br />sample:  0.0538807741<br />change:  5.388077e-02<br />stock: IBM","theoretical:  0.018488116<br />sample:  0.0541313302<br />change:  5.413133e-02<br />stock: IBM","theoretical:  0.019575788<br />sample:  0.0554746854<br />change:  5.547469e-02<br />stock: IBM","theoretical:  0.020663482<br />sample:  0.0557543121<br />change:  5.575431e-02<br />stock: IBM","theoretical:  0.021751201<br />sample:  0.0562471455<br />change:  5.624715e-02<br />stock: IBM","theoretical:  0.022838946<br />sample:  0.0593921541<br />change:  5.939215e-02<br />stock: IBM","theoretical:  0.023926717<br />sample:  0.0613598673<br />change:  6.135987e-02<br />stock: IBM","theoretical:  0.025014517<br />sample:  0.0614358968<br />change:  6.143590e-02<br />stock: IBM","theoretical:  0.026102347<br />sample:  0.0621442422<br />change:  6.214424e-02<br />stock: IBM","theoretical:  0.027190208<br />sample:  0.0635647773<br />change:  6.356478e-02<br />stock: IBM","theoretical:  0.028278100<br />sample:  0.0655086342<br />change:  6.550863e-02<br />stock: IBM","theoretical:  0.029366026<br />sample:  0.0659187420<br />change:  6.591874e-02<br />stock: IBM","theoretical:  0.030453987<br />sample:  0.0673785634<br />change:  6.737856e-02<br />stock: IBM","theoretical:  0.031541984<br />sample:  0.0675841370<br />change:  6.758414e-02<br />stock: IBM","theoretical:  0.032630019<br />sample:  0.0706541023<br />change:  7.065410e-02<br />stock: IBM","theoretical:  0.033718091<br />sample:  0.0707629413<br />change:  7.076294e-02<br />stock: IBM","theoretical:  0.034806204<br />sample:  0.0708301077<br />change:  7.083011e-02<br />stock: IBM","theoretical:  0.035894358<br />sample:  0.0722354452<br />change:  7.223545e-02<br />stock: IBM","theoretical:  0.036982555<br />sample:  0.0743138467<br />change:  7.431385e-02<br />stock: IBM","theoretical:  0.038070795<br />sample:  0.0759038610<br />change:  7.590386e-02<br />stock: IBM","theoretical:  0.039159081<br />sample:  0.0759341862<br />change:  7.593419e-02<br />stock: IBM","theoretical:  0.040247412<br />sample:  0.0764625098<br />change:  7.646251e-02<br />stock: IBM","theoretical:  0.041335792<br />sample:  0.0803711464<br />change:  8.037115e-02<br />stock: IBM","theoretical:  0.042424220<br />sample:  0.0809289891<br />change:  8.092899e-02<br />stock: IBM","theoretical:  0.043512699<br />sample:  0.0822685220<br />change:  8.226852e-02<br />stock: IBM","theoretical:  0.044601229<br />sample:  0.0880039960<br />change:  8.800400e-02<br />stock: IBM","theoretical:  0.045689813<br />sample:  0.0885650990<br />change:  8.856510e-02<br />stock: IBM","theoretical:  0.046778450<br />sample:  0.0889529988<br />change:  8.895300e-02<br />stock: IBM","theoretical:  0.047867143<br />sample:  0.0932925700<br />change:  9.329257e-02<br />stock: IBM","theoretical:  0.048955892<br />sample:  0.0937181617<br />change:  9.371816e-02<br />stock: IBM","theoretical:  0.050044699<br />sample:  0.0939792221<br />change:  9.397922e-02<br />stock: IBM","theoretical:  0.051133566<br />sample:  0.0949380671<br />change:  9.493807e-02<br />stock: IBM","theoretical:  0.052222494<br />sample:  0.0950601681<br />change:  9.506017e-02<br />stock: IBM","theoretical:  0.053311483<br />sample:  0.0993242637<br />change:  9.932426e-02<br />stock: IBM","theoretical:  0.054400536<br />sample:  0.1001913420<br />change:  1.001913e-01<br />stock: IBM","theoretical:  0.055489653<br />sample:  0.1011119159<br />change:  1.011119e-01<br />stock: IBM","theoretical:  0.056578836<br />sample:  0.1023703673<br />change:  1.023704e-01<br />stock: IBM","theoretical:  0.057668086<br />sample:  0.1032192983<br />change:  1.032193e-01<br />stock: IBM","theoretical:  0.058757404<br />sample:  0.1035648886<br />change:  1.035649e-01<br />stock: IBM","theoretical:  0.059846793<br />sample:  0.1036126425<br />change:  1.036126e-01<br />stock: IBM","theoretical:  0.060936252<br />sample:  0.1038944248<br />change:  1.038944e-01<br />stock: IBM","theoretical:  0.062025783<br />sample:  0.1039375556<br />change:  1.039376e-01<br />stock: IBM","theoretical:  0.063115389<br />sample:  0.1072936203<br />change:  1.072936e-01<br />stock: IBM","theoretical:  0.064205069<br />sample:  0.1077674394<br />change:  1.077674e-01<br />stock: IBM","theoretical:  0.065294825<br />sample:  0.1078728494<br />change:  1.078728e-01<br />stock: IBM","theoretical:  0.066384659<br />sample:  0.1082526671<br />change:  1.082527e-01<br />stock: IBM","theoretical:  0.067474572<br />sample:  0.1084919635<br />change:  1.084920e-01<br />stock: IBM","theoretical:  0.068564565<br />sample:  0.1085348289<br />change:  1.085348e-01<br />stock: IBM","theoretical:  0.069654639<br />sample:  0.1108504757<br />change:  1.108505e-01<br />stock: IBM","theoretical:  0.070744796<br />sample:  0.1129368662<br />change:  1.129369e-01<br />stock: IBM","theoretical:  0.071835038<br />sample:  0.1144653792<br />change:  1.144654e-01<br />stock: IBM","theoretical:  0.072925364<br />sample:  0.1150149314<br />change:  1.150149e-01<br />stock: IBM","theoretical:  0.074015778<br />sample:  0.1157595129<br />change:  1.157595e-01<br />stock: IBM","theoretical:  0.075106279<br />sample:  0.1174596774<br />change:  1.174597e-01<br />stock: IBM","theoretical:  0.076196870<br />sample:  0.1182498235<br />change:  1.182498e-01<br />stock: IBM","theoretical:  0.077287551<br />sample:  0.1187733722<br />change:  1.187734e-01<br />stock: IBM","theoretical:  0.078378325<br />sample:  0.1208896750<br />change:  1.208897e-01<br />stock: IBM","theoretical:  0.079469191<br />sample:  0.1210739829<br />change:  1.210740e-01<br />stock: IBM","theoretical:  0.080560152<br />sample:  0.1217137709<br />change:  1.217138e-01<br />stock: IBM","theoretical:  0.081651209<br />sample:  0.1235603529<br />change:  1.235604e-01<br />stock: IBM","theoretical:  0.082742364<br />sample:  0.1241945828<br />change:  1.241946e-01<br />stock: IBM","theoretical:  0.083833616<br />sample:  0.1243449218<br />change:  1.243449e-01<br />stock: IBM","theoretical:  0.084924969<br />sample:  0.1244402927<br />change:  1.244403e-01<br />stock: IBM","theoretical:  0.086016423<br />sample:  0.1278246192<br />change:  1.278246e-01<br />stock: IBM","theoretical:  0.087107979<br />sample:  0.1290320034<br />change:  1.290320e-01<br />stock: IBM","theoretical:  0.088199639<br />sample:  0.1298971222<br />change:  1.298971e-01<br />stock: IBM","theoretical:  0.089291404<br />sample:  0.1305373669<br />change:  1.305374e-01<br />stock: IBM","theoretical:  0.090383276<br />sample:  0.1305569599<br />change:  1.305570e-01<br />stock: IBM","theoretical:  0.091475255<br />sample:  0.1307510435<br />change:  1.307510e-01<br />stock: IBM","theoretical:  0.092567343<br />sample:  0.1312433892<br />change:  1.312434e-01<br />stock: IBM","theoretical:  0.093659542<br />sample:  0.1358450892<br />change:  1.358451e-01<br />stock: IBM","theoretical:  0.094751853<br />sample:  0.1360461084<br />change:  1.360461e-01<br />stock: IBM","theoretical:  0.095844277<br />sample:  0.1377686611<br />change:  1.377687e-01<br />stock: IBM","theoretical:  0.096936815<br />sample:  0.1399857220<br />change:  1.399857e-01<br />stock: IBM","theoretical:  0.098029468<br />sample:  0.1400316462<br />change:  1.400316e-01<br />stock: IBM","theoretical:  0.099122239<br />sample:  0.1401481237<br />change:  1.401481e-01<br />stock: IBM","theoretical:  0.100215128<br />sample:  0.1408423746<br />change:  1.408424e-01<br />stock: IBM","theoretical:  0.101308137<br />sample:  0.1419399201<br />change:  1.419399e-01<br />stock: IBM","theoretical:  0.102401267<br />sample:  0.1440866354<br />change:  1.440866e-01<br />stock: IBM","theoretical:  0.103494520<br />sample:  0.1441702779<br />change:  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IBM","theoretical:  0.126483460<br />sample:  0.1713274421<br />change:  1.713274e-01<br />stock: IBM","theoretical:  0.127579744<br />sample:  0.1717156384<br />change:  1.717156e-01<br />stock: IBM","theoretical:  0.128676182<br />sample:  0.1727431376<br />change:  1.727431e-01<br />stock: IBM","theoretical:  0.129772774<br />sample:  0.1742140541<br />change:  1.742141e-01<br />stock: IBM","theoretical:  0.130869522<br />sample:  0.1743020819<br />change:  1.743021e-01<br />stock: IBM","theoretical:  0.131966428<br />sample:  0.1766199390<br />change:  1.766199e-01<br />stock: IBM","theoretical:  0.133063493<br />sample:  0.1782436225<br />change:  1.782436e-01<br />stock: IBM","theoretical:  0.134160717<br />sample:  0.1785145207<br />change:  1.785145e-01<br />stock: IBM","theoretical:  0.135258104<br />sample:  0.1791249806<br />change:  1.791250e-01<br />stock: IBM","theoretical:  0.136355653<br />sample:  0.1817204391<br />change:  1.817204e-01<br />stock: IBM","theoretical:  0.137453366<br />sample:  0.1824508108<br />change:  1.824508e-01<br />stock: IBM","theoretical:  0.138551245<br />sample:  0.1832852698<br />change:  1.832853e-01<br />stock: IBM","theoretical:  0.139649291<br />sample:  0.1839409641<br />change:  1.839410e-01<br />stock: IBM","theoretical:  0.140747506<br />sample:  0.1854323113<br />change:  1.854323e-01<br />stock: IBM","theoretical:  0.141845890<br />sample:  0.1856150617<br />change:  1.856151e-01<br />stock: IBM","theoretical:  0.142944446<br />sample:  0.1867420397<br />change:  1.867420e-01<br />stock: IBM","theoretical:  0.144043174<br />sample:  0.1887129940<br />change:  1.887130e-01<br />stock: IBM","theoretical:  0.145142076<br />sample:  0.1892078690<br />change:  1.892079e-01<br />stock: IBM","theoretical:  0.146241153<br />sample:  0.1894151447<br />change:  1.894151e-01<br />stock: IBM","theoretical:  0.147340407<br />sample:  0.1903476909<br />change:  1.903477e-01<br />stock: IBM","theoretical:  0.148439839<br />sample:  0.1914148508<br />change:  1.914149e-01<br />stock: IBM","theoretical:  0.149539450<br />sample:  0.1927825834<br />change:  1.927826e-01<br />stock: IBM","theoretical:  0.150639242<br />sample:  0.1934654969<br />change:  1.934655e-01<br />stock: IBM","theoretical:  0.151739217<br />sample:  0.1941926581<br />change:  1.941927e-01<br />stock: IBM","theoretical:  0.152839375<br />sample:  0.1942542763<br />change:  1.942543e-01<br />stock: IBM","theoretical:  0.153939718<br />sample:  0.1958381628<br />change:  1.958382e-01<br />stock: IBM","theoretical:  0.155040248<br />sample:  0.1961069087<br />change:  1.961069e-01<br />stock: IBM","theoretical:  0.156140965<br />sample:  0.1977954276<br />change:  1.977954e-01<br />stock: IBM","theoretical:  0.157241872<br />sample:  0.1985058368<br />change:  1.985058e-01<br />stock: IBM","theoretical:  0.158342969<br />sample:  0.1990890663<br />change:  1.990891e-01<br />stock: IBM","theoretical:  0.159444258<br />sample:  0.1998821754<br />change:  1.998822e-01<br />stock: IBM","theoretical:  0.160545741<br />sample:  0.2005912193<br />change:  2.005912e-01<br />stock: IBM","theoretical:  0.161647418<br />sample:  0.2009011357<br />change:  2.009011e-01<br />stock: IBM","theoretical:  0.162749292<br />sample:  0.2022799871<br />change:  2.022800e-01<br />stock: IBM","theoretical:  0.163851363<br />sample:  0.2029470344<br />change:  2.029470e-01<br />stock: IBM","theoretical:  0.164953633<br />sample:  0.2035908793<br />change:  2.035909e-01<br />stock: IBM","theoretical:  0.166056104<br />sample:  0.2055847149<br />change:  2.055847e-01<br />stock: IBM","theoretical:  0.167158777<br />sample:  0.2056341845<br />change:  2.056342e-01<br />stock: IBM","theoretical:  0.168261653<br />sample:  0.2067403307<br />change:  2.067403e-01<br />stock: IBM","theoretical:  0.169364733<br />sample:  0.2070194481<br />change:  2.070194e-01<br />stock: IBM","theoretical:  0.170468020<br />sample:  0.2072289274<br />change:  2.072289e-01<br />stock: IBM","theoretical:  0.171571514<br />sample:  0.2072734573<br />change:  2.072735e-01<br />stock: IBM","theoretical:  0.172675218<br />sample:  0.2094477171<br />change:  2.094477e-01<br />stock: IBM","theoretical:  0.173779131<br />sample:  0.2096998372<br />change:  2.096998e-01<br />stock: IBM","theoretical:  0.174883257<br />sample:  0.2114200906<br />change:  2.114201e-01<br />stock: IBM","theoretical:  0.175987596<br />sample:  0.2154235221<br />change:  2.154235e-01<br />stock: IBM","theoretical:  0.177092149<br />sample:  0.2163566711<br />change:  2.163567e-01<br />stock: IBM","theoretical:  0.178196918<br />sample:  0.2180640622<br />change:  2.180641e-01<br />stock: IBM","theoretical:  0.179301905<br />sample:  0.2182143297<br />change:  2.182143e-01<br />stock: IBM","theoretical:  0.180407111<br />sample:  0.2188426053<br />change:  2.188426e-01<br />stock: IBM","theoretical:  0.181512538<br />sample:  0.2206273278<br />change:  2.206273e-01<br />stock: IBM","theoretical:  0.182618186<br />sample:  0.2220804835<br />change:  2.220805e-01<br />stock: IBM","theoretical:  0.183724058<br />sample:  0.2236585909<br />change:  2.236586e-01<br />stock: IBM","theoretical:  0.184830154<br />sample:  0.2237247897<br />change:  2.237248e-01<br />stock: IBM","theoretical:  0.185936476<br />sample:  0.2278121871<br />change:  2.278122e-01<br />stock: IBM","theoretical:  0.187043026<br />sample:  0.2283813207<br />change:  2.283813e-01<br />stock: IBM","theoretical:  0.188149805<br />sample:  0.2294230493<br />change:  2.294230e-01<br />stock: IBM","theoretical:  0.189256815<br />sample:  0.2319690177<br />change:  2.319690e-01<br />stock: IBM","theoretical:  0.190364057<br />sample:  0.2331220085<br />change:  2.331220e-01<br />stock: IBM","theoretical:  0.191471532<br />sample:  0.2343998400<br />change:  2.343998e-01<br />stock: IBM","theoretical:  0.192579242<br />sample:  0.2345869041<br />change:  2.345869e-01<br 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IBM","theoretical:  0.204779973<br />sample:  0.2545826789<br />change:  2.545827e-01<br />stock: IBM","theoretical:  0.205890616<br />sample:  0.2570164723<br />change:  2.570165e-01<br />stock: IBM","theoretical:  0.207001513<br />sample:  0.2585474814<br />change:  2.585475e-01<br />stock: IBM","theoretical:  0.208112666<br />sample:  0.2590567532<br />change:  2.590568e-01<br />stock: IBM","theoretical:  0.209224075<br />sample:  0.2606596765<br />change:  2.606597e-01<br />stock: IBM","theoretical:  0.210335744<br />sample:  0.2621928326<br />change:  2.621928e-01<br />stock: IBM","theoretical:  0.211447672<br />sample:  0.2628698605<br />change:  2.628699e-01<br />stock: IBM","theoretical:  0.212559861<br />sample:  0.2633719437<br />change:  2.633719e-01<br />stock: IBM","theoretical:  0.213672314<br />sample:  0.2635023510<br />change:  2.635024e-01<br />stock: IBM","theoretical:  0.214785031<br />sample:  0.2655737338<br />change:  2.655737e-01<br />stock: IBM","theoretical:  0.215898014<br />sample:  0.2664600286<br />change:  2.664600e-01<br />stock: IBM","theoretical:  0.217011265<br />sample:  0.2671797307<br />change:  2.671797e-01<br />stock: IBM","theoretical:  0.218124784<br />sample:  0.2672776551<br />change:  2.672777e-01<br />stock: IBM","theoretical:  0.219238574<br />sample:  0.2675885796<br />change:  2.675886e-01<br />stock: IBM","theoretical:  0.220352637<br />sample:  0.2690556479<br />change:  2.690556e-01<br />stock: IBM","theoretical:  0.221466972<br />sample:  0.2704982290<br />change:  2.704982e-01<br />stock: IBM","theoretical:  0.222581583<br />sample:  0.2727107821<br />change:  2.727108e-01<br />stock: IBM","theoretical:  0.223696471<br />sample:  0.2748670517<br />change:  2.748671e-01<br />stock: IBM","theoretical:  0.224811636<br />sample:  0.2759866036<br />change:  2.759866e-01<br />stock: IBM","theoretical:  0.225927081<br />sample:  0.2767114074<br />change:  2.767114e-01<br />stock: IBM","theoretical:  0.227042808<br 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0.2911800924<br />change:  2.911801e-01<br />stock: IBM","theoretical:  0.239334795<br />sample:  0.2962330018<br />change:  2.962330e-01<br />stock: IBM","theoretical:  0.240454015<br />sample:  0.2968203195<br />change:  2.968203e-01<br />stock: IBM","theoretical:  0.241573537<br />sample:  0.3005052084<br />change:  3.005052e-01<br />stock: IBM","theoretical:  0.242693362<br />sample:  0.3010735638<br />change:  3.010736e-01<br />stock: IBM","theoretical:  0.243813491<br />sample:  0.3021216149<br />change:  3.021216e-01<br />stock: IBM","theoretical:  0.244933926<br />sample:  0.3027430056<br />change:  3.027430e-01<br />stock: IBM","theoretical:  0.246054669<br />sample:  0.3042473899<br />change:  3.042474e-01<br />stock: IBM","theoretical:  0.247175721<br />sample:  0.3075629994<br />change:  3.075630e-01<br />stock: IBM","theoretical:  0.248297084<br />sample:  0.3088973019<br />change:  3.088973e-01<br />stock: IBM","theoretical:  0.249418759<br />sample:  0.3102590271<br />change:  3.102590e-01<br />stock: IBM","theoretical:  0.250540747<br />sample:  0.3113090363<br />change:  3.113090e-01<br />stock: IBM","theoretical:  0.251663052<br />sample:  0.3117457615<br />change:  3.117458e-01<br />stock: IBM","theoretical:  0.252785673<br />sample:  0.3124071217<br />change:  3.124071e-01<br />stock: IBM","theoretical:  0.253908613<br />sample:  0.3140971213<br />change:  3.140971e-01<br />stock: IBM","theoretical:  0.255031873<br />sample:  0.3143677848<br />change:  3.143678e-01<br />stock: IBM","theoretical:  0.256155456<br />sample:  0.3166745385<br />change:  3.166745e-01<br />stock: IBM","theoretical:  0.257279361<br />sample:  0.3192901792<br />change:  3.192902e-01<br />stock: IBM","theoretical:  0.258403592<br />sample:  0.3196853593<br />change:  3.196854e-01<br />stock: IBM","theoretical:  0.259528149<br />sample:  0.3203183470<br />change:  3.203183e-01<br />stock: IBM","theoretical:  0.260653035<br />sample:  0.3204836687<br />change:  3.204837e-01<br />stock: IBM","theoretical:  0.261778251<br />sample:  0.3213377652<br />change:  3.213378e-01<br />stock: IBM","theoretical:  0.262903798<br />sample:  0.3217800375<br />change:  3.217800e-01<br />stock: IBM","theoretical:  0.264029678<br />sample:  0.3222087107<br />change:  3.222087e-01<br />stock: IBM","theoretical:  0.265155894<br />sample:  0.3227591533<br />change:  3.227592e-01<br />stock: IBM","theoretical:  0.266282445<br />sample:  0.3229417540<br />change:  3.229418e-01<br />stock: IBM","theoretical:  0.267409335<br />sample:  0.3249632975<br />change:  3.249633e-01<br />stock: IBM","theoretical:  0.268536564<br />sample:  0.3249777568<br />change:  3.249778e-01<br />stock: IBM","theoretical:  0.269664135<br />sample:  0.3256114035<br />change:  3.256114e-01<br />stock: IBM","theoretical:  0.270792048<br />sample:  0.3265160476<br />change:  3.265160e-01<br />stock: IBM","theoretical:  0.271920306<br />sample:  0.3266051533<br />change:  3.266052e-01<br />stock: IBM","theoretical:  0.273048911<br />sample:  0.3275858177<br />change:  3.275858e-01<br />stock: IBM","theoretical:  0.274177863<br />sample:  0.3288743802<br />change:  3.288744e-01<br />stock: IBM","theoretical:  0.275307165<br />sample:  0.3296251023<br />change:  3.296251e-01<br />stock: IBM","theoretical:  0.276436818<br />sample:  0.3333378403<br />change:  3.333378e-01<br />stock: IBM","theoretical:  0.277566824<br />sample:  0.3413505673<br />change:  3.413506e-01<br />stock: IBM","theoretical:  0.278697184<br />sample:  0.3427239850<br />change:  3.427240e-01<br />stock: IBM","theoretical:  0.279827901<br />sample:  0.3434316285<br />change:  3.434316e-01<br />stock: IBM","theoretical:  0.280958976<br />sample:  0.3438939382<br />change:  3.438939e-01<br />stock: IBM","theoretical:  0.282090410<br />sample:  0.3466651446<br />change:  3.466651e-01<br />stock: IBM","theoretical:  0.283222205<br />sample:  0.3488523947<br />change:  3.488524e-01<br />stock: IBM","theoretical:  0.284354364<br />sample:  0.3488956123<br />change:  3.488956e-01<br />stock: IBM","theoretical:  0.285486886<br />sample:  0.3490483427<br />change:  3.490483e-01<br />stock: IBM","theoretical:  0.286619776<br />sample:  0.3491350823<br />change:  3.491351e-01<br />stock: IBM","theoretical:  0.287753033<br />sample:  0.3495279204<br />change:  3.495279e-01<br />stock: IBM","theoretical:  0.288886660<br />sample:  0.3500600695<br />change:  3.500601e-01<br />stock: IBM","theoretical:  0.290020658<br />sample:  0.3527137756<br />change:  3.527138e-01<br />stock: IBM","theoretical:  0.291155029<br />sample:  0.3595491000<br />change:  3.595491e-01<br />stock: IBM","theoretical:  0.292289775<br />sample:  0.3600067857<br />change:  3.600068e-01<br />stock: IBM","theoretical:  0.293424898<br />sample:  0.3600892095<br />change:  3.600892e-01<br />stock: IBM","theoretical:  0.294560398<br />sample:  0.3603635754<br />change:  3.603636e-01<br />stock: IBM","theoretical:  0.295696279<br />sample:  0.3610719194<br />change:  3.610719e-01<br />stock: IBM","theoretical:  0.296832541<br />sample:  0.3611023726<br />change:  3.611024e-01<br />stock: IBM","theoretical:  0.297969187<br />sample:  0.3628162423<br />change:  3.628162e-01<br />stock: IBM","theoretical:  0.299106218<br />sample:  0.3636741791<br />change:  3.636742e-01<br />stock: IBM","theoretical:  0.300243635<br />sample:  0.3644675383<br />change:  3.644675e-01<br />stock: IBM","theoretical:  0.301381442<br />sample:  0.3647585559<br />change:  3.647586e-01<br />stock: IBM","theoretical:  0.302519638<br />sample:  0.3653137279<br />change:  3.653137e-01<br />stock: IBM","theoretical:  0.303658227<br />sample:  0.3654888198<br />change:  3.654888e-01<br />stock: IBM","theoretical:  0.304797209<br />sample:  0.3670610859<br />change:  3.670611e-01<br />stock: IBM","theoretical:  0.305936587<br />sample:  0.3683424516<br />change:  3.683425e-01<br />stock: IBM","theoretical:  0.307076362<br 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0.3852702565<br />change:  3.852703e-01<br />stock: IBM","theoretical:  0.319640616<br />sample:  0.3887808488<br />change:  3.887808e-01<br />stock: IBM","theoretical:  0.320785298<br />sample:  0.3908364409<br />change:  3.908364e-01<br />stock: IBM","theoretical:  0.321930399<br />sample:  0.3918014208<br />change:  3.918014e-01<br />stock: IBM","theoretical:  0.323075923<br />sample:  0.3921976201<br />change:  3.921976e-01<br />stock: IBM","theoretical:  0.324221871<br />sample:  0.3929848534<br />change:  3.929849e-01<br />stock: IBM","theoretical:  0.325368245<br />sample:  0.3930060962<br />change:  3.930061e-01<br />stock: IBM","theoretical:  0.326515046<br />sample:  0.3938866427<br />change:  3.938866e-01<br />stock: IBM","theoretical:  0.327662278<br />sample:  0.3947934920<br />change:  3.947935e-01<br />stock: IBM","theoretical:  0.328809940<br />sample:  0.3953577808<br />change:  3.953578e-01<br />stock: IBM","theoretical:  0.329958036<br />sample:  0.3958409362<br />change:  3.958409e-01<br />stock: IBM","theoretical:  0.331106567<br />sample:  0.3959415826<br />change:  3.959416e-01<br />stock: IBM","theoretical:  0.332255535<br />sample:  0.3967098330<br />change:  3.967098e-01<br />stock: IBM","theoretical:  0.333404942<br />sample:  0.3970884931<br />change:  3.970885e-01<br />stock: IBM","theoretical:  0.334554789<br />sample:  0.4003158615<br />change:  4.003159e-01<br />stock: IBM","theoretical:  0.335705079<br />sample:  0.4005223270<br />change:  4.005223e-01<br />stock: IBM","theoretical:  0.336855813<br />sample:  0.4010211405<br />change:  4.010211e-01<br />stock: IBM","theoretical:  0.338006994<br />sample:  0.4022205774<br />change:  4.022206e-01<br />stock: IBM","theoretical:  0.339158622<br />sample:  0.4026498950<br />change:  4.026499e-01<br />stock: IBM","theoretical:  0.340310701<br />sample:  0.4053835600<br />change:  4.053836e-01<br />stock: IBM","theoretical:  0.341463231<br />sample:  0.4054160246<br />change:  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0.377426289<br />sample:  0.4420440904<br />change:  4.420441e-01<br />stock: IBM","theoretical:  0.378594302<br />sample:  0.4422539560<br />change:  4.422540e-01<br />stock: IBM","theoretical:  0.379762832<br />sample:  0.4431343908<br />change:  4.431344e-01<br />stock: IBM","theoretical:  0.380931880<br />sample:  0.4439136904<br />change:  4.439137e-01<br />stock: IBM","theoretical:  0.382101449<br />sample:  0.4442716750<br />change:  4.442717e-01<br />stock: IBM","theoretical:  0.383271541<br />sample:  0.4447789660<br />change:  4.447790e-01<br />stock: IBM","theoretical:  0.384442158<br />sample:  0.4470461659<br />change:  4.470462e-01<br />stock: IBM","theoretical:  0.385613302<br />sample:  0.4470689487<br />change:  4.470689e-01<br />stock: IBM","theoretical:  0.386784975<br />sample:  0.4470780698<br />change:  4.470781e-01<br />stock: IBM","theoretical:  0.387957180<br />sample:  0.4495878261<br />change:  4.495878e-01<br />stock: IBM","theoretical:  0.389129917<br 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0.4612339281<br />change:  4.612339e-01<br />stock: IBM","theoretical:  0.402065836<br />sample:  0.4612826950<br />change:  4.612827e-01<br />stock: IBM","theoretical:  0.403245139<br />sample:  0.4614119638<br />change:  4.614120e-01<br />stock: IBM","theoretical:  0.404425003<br />sample:  0.4631864660<br />change:  4.631865e-01<br />stock: IBM","theoretical:  0.405605431<br />sample:  0.4651209474<br />change:  4.651209e-01<br />stock: IBM","theoretical:  0.406786424<br />sample:  0.4688524662<br />change:  4.688525e-01<br />stock: IBM","theoretical:  0.407967984<br />sample:  0.4727730065<br />change:  4.727730e-01<br />stock: IBM","theoretical:  0.409150114<br />sample:  0.4751165181<br />change:  4.751165e-01<br />stock: IBM","theoretical:  0.410332817<br />sample:  0.4756549749<br />change:  4.756550e-01<br />stock: IBM","theoretical:  0.411516093<br />sample:  0.4773487640<br />change:  4.773488e-01<br />stock: IBM","theoretical:  0.412699946<br />sample:  0.4779735186<br 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4.927373e-01<br />stock: IBM","theoretical:  0.425761017<br />sample:  0.4932156224<br />change:  4.932156e-01<br />stock: IBM","theoretical:  0.426951963<br />sample:  0.4940255403<br />change:  4.940255e-01<br />stock: IBM","theoretical:  0.428143514<br />sample:  0.4954736380<br />change:  4.954736e-01<br />stock: IBM","theoretical:  0.429335674<br />sample:  0.4955421804<br />change:  4.955422e-01<br />stock: IBM","theoretical:  0.430528445<br />sample:  0.4966008868<br />change:  4.966009e-01<br />stock: IBM","theoretical:  0.431721828<br />sample:  0.4975125873<br />change:  4.975126e-01<br />stock: IBM","theoretical:  0.432915826<br />sample:  0.4976827772<br />change:  4.976828e-01<br />stock: IBM","theoretical:  0.434110442<br />sample:  0.4978987235<br />change:  4.978987e-01<br />stock: IBM","theoretical:  0.435305678<br />sample:  0.4990848803<br />change:  4.990849e-01<br />stock: IBM","theoretical:  0.436501536<br />sample:  0.5000039937<br />change:  5.000040e-01<br 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IBM","theoretical:  0.449697719<br />sample:  0.5171058706<br />change:  5.171059e-01<br />stock: IBM","theoretical:  0.450901229<br />sample:  0.5184866168<br />change:  5.184866e-01<br />stock: IBM","theoretical:  0.452105393<br />sample:  0.5219684519<br />change:  5.219685e-01<br />stock: IBM","theoretical:  0.453310213<br />sample:  0.5220657765<br />change:  5.220658e-01<br />stock: IBM","theoretical:  0.454515691<br />sample:  0.5228354934<br />change:  5.228355e-01<br />stock: IBM","theoretical:  0.455721830<br />sample:  0.5263836239<br />change:  5.263836e-01<br />stock: IBM","theoretical:  0.456928633<br />sample:  0.5272717277<br />change:  5.272717e-01<br />stock: IBM","theoretical:  0.458136101<br />sample:  0.5306147319<br />change:  5.306147e-01<br />stock: IBM","theoretical:  0.459344238<br />sample:  0.5322068477<br />change:  5.322068e-01<br />stock: IBM","theoretical:  0.460553045<br />sample:  0.5331958945<br />change:  5.331959e-01<br />stock: IBM","theoretical:  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IBM","theoretical:  0.536919515<br />sample:  0.6221439169<br />change:  6.221439e-01<br />stock: IBM","theoretical:  0.538176023<br />sample:  0.6221622711<br />change:  6.221623e-01<br />stock: IBM","theoretical:  0.539433382<br />sample:  0.6222863159<br />change:  6.222863e-01<br />stock: IBM","theoretical:  0.540691594<br />sample:  0.6243131072<br />change:  6.243131e-01<br />stock: IBM","theoretical:  0.541950662<br />sample:  0.6252434370<br />change:  6.252434e-01<br />stock: IBM","theoretical:  0.543210591<br />sample:  0.6264482668<br />change:  6.264483e-01<br />stock: IBM","theoretical:  0.544471382<br />sample:  0.6283216138<br />change:  6.283216e-01<br />stock: IBM","theoretical:  0.545733039<br />sample:  0.6319372531<br />change:  6.319373e-01<br />stock: IBM","theoretical:  0.546995565<br />sample:  0.6384249022<br />change:  6.384249e-01<br />stock: IBM","theoretical:  0.548258964<br />sample:  0.6399097891<br />change:  6.399098e-01<br />stock: IBM","theoretical:  0.549523239<br />sample:  0.6409555292<br />change:  6.409555e-01<br />stock: IBM","theoretical:  0.550788393<br />sample:  0.6460502234<br />change:  6.460502e-01<br />stock: IBM","theoretical:  0.552054429<br />sample:  0.6473827910<br />change:  6.473828e-01<br />stock: IBM","theoretical:  0.553321350<br />sample:  0.6480020144<br />change:  6.480020e-01<br />stock: IBM","theoretical:  0.554589160<br />sample:  0.6480250999<br />change:  6.480251e-01<br />stock: IBM","theoretical:  0.555857863<br />sample:  0.6497928892<br />change:  6.497929e-01<br />stock: IBM","theoretical:  0.557127460<br />sample:  0.6506804290<br />change:  6.506804e-01<br />stock: IBM","theoretical:  0.558397956<br />sample:  0.6519343617<br />change:  6.519344e-01<br />stock: IBM","theoretical:  0.559669354<br />sample:  0.6530515581<br />change:  6.530516e-01<br />stock: IBM","theoretical:  0.560941658<br />sample:  0.6571202088<br />change:  6.571202e-01<br />stock: IBM","theoretical:  0.562214870<br 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0.6761732570<br />change:  6.761733e-01<br />stock: IBM","theoretical:  0.576281149<br />sample:  0.6773658159<br />change:  6.773658e-01<br />stock: IBM","theoretical:  0.577565531<br />sample:  0.6780536693<br />change:  6.780537e-01<br />stock: IBM","theoretical:  0.578850868<br />sample:  0.6806427517<br />change:  6.806428e-01<br />stock: IBM","theoretical:  0.580137161<br />sample:  0.6894667599<br />change:  6.894668e-01<br />stock: IBM","theoretical:  0.581424414<br />sample:  0.6898219089<br />change:  6.898219e-01<br />stock: IBM","theoretical:  0.582712632<br />sample:  0.6903503747<br />change:  6.903504e-01<br />stock: IBM","theoretical:  0.584001818<br />sample:  0.6925751272<br />change:  6.925751e-01<br />stock: IBM","theoretical:  0.585291975<br />sample:  0.6926488225<br />change:  6.926488e-01<br />stock: IBM","theoretical:  0.586583107<br />sample:  0.6933349953<br />change:  6.933350e-01<br />stock: IBM","theoretical:  0.587875217<br />sample:  0.6934291624<br />change:  6.934292e-01<br />stock: IBM","theoretical:  0.589168310<br />sample:  0.6940514450<br />change:  6.940514e-01<br />stock: IBM","theoretical:  0.590462389<br />sample:  0.6947963184<br />change:  6.947963e-01<br />stock: IBM","theoretical:  0.591757457<br />sample:  0.6970429797<br />change:  6.970430e-01<br />stock: IBM","theoretical:  0.593053518<br />sample:  0.6981366204<br />change:  6.981366e-01<br />stock: IBM","theoretical:  0.594350577<br />sample:  0.6982649223<br />change:  6.982649e-01<br />stock: IBM","theoretical:  0.595648636<br />sample:  0.6987275682<br />change:  6.987276e-01<br />stock: IBM","theoretical:  0.596947700<br />sample:  0.6993935747<br />change:  6.993936e-01<br />stock: IBM","theoretical:  0.598247771<br />sample:  0.6994378015<br />change:  6.994378e-01<br />stock: IBM","theoretical:  0.599548855<br />sample:  0.6995202621<br />change:  6.995203e-01<br />stock: IBM","theoretical:  0.600850954<br />sample:  0.7030864632<br />change:  7.030865e-01<br />stock: IBM","theoretical:  0.602154073<br />sample:  0.7035913574<br />change:  7.035914e-01<br />stock: IBM","theoretical:  0.603458215<br />sample:  0.7045161977<br />change:  7.045162e-01<br />stock: IBM","theoretical:  0.604763385<br />sample:  0.7045995548<br />change:  7.045996e-01<br />stock: IBM","theoretical:  0.606069585<br />sample:  0.7073025577<br />change:  7.073026e-01<br />stock: IBM","theoretical:  0.607376821<br />sample:  0.7079093223<br />change:  7.079093e-01<br />stock: IBM","theoretical:  0.608685095<br />sample:  0.7098793261<br />change:  7.098793e-01<br />stock: IBM","theoretical:  0.609994411<br />sample:  0.7138962134<br />change:  7.138962e-01<br />stock: IBM","theoretical:  0.611304774<br />sample:  0.7160416132<br />change:  7.160416e-01<br />stock: IBM","theoretical:  0.612616188<br />sample:  0.7171665257<br />change:  7.171665e-01<br />stock: IBM","theoretical:  0.613928656<br />sample:  0.7183649419<br />change:  7.183649e-01<br 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IBM","theoretical:  0.628436543<br />sample:  0.7352198142<br />change:  7.352198e-01<br />stock: IBM","theoretical:  0.629761978<br />sample:  0.7358785189<br />change:  7.358785e-01<br />stock: IBM","theoretical:  0.631088521<br />sample:  0.7363520933<br />change:  7.363521e-01<br />stock: IBM","theoretical:  0.632416175<br />sample:  0.7371468296<br />change:  7.371468e-01<br />stock: IBM","theoretical:  0.633744944<br />sample:  0.7377826189<br />change:  7.377826e-01<br />stock: IBM","theoretical:  0.635074834<br />sample:  0.7394303808<br />change:  7.394304e-01<br />stock: IBM","theoretical:  0.636405847<br />sample:  0.7399311047<br />change:  7.399311e-01<br />stock: IBM","theoretical:  0.637737990<br />sample:  0.7426097489<br />change:  7.426097e-01<br />stock: IBM","theoretical:  0.639071264<br />sample:  0.7429237872<br />change:  7.429238e-01<br />stock: IBM","theoretical:  0.640405676<br />sample:  0.7431120498<br />change:  7.431120e-01<br />stock: IBM","theoretical:  0.641741229<br />sample:  0.7440339595<br />change:  7.440340e-01<br />stock: IBM","theoretical:  0.643077928<br />sample:  0.7465934375<br />change:  7.465934e-01<br />stock: IBM","theoretical:  0.644415777<br />sample:  0.7472613751<br />change:  7.472614e-01<br />stock: IBM","theoretical:  0.645754780<br />sample:  0.7478961509<br />change:  7.478962e-01<br />stock: IBM","theoretical:  0.647094942<br />sample:  0.7491285352<br />change:  7.491285e-01<br />stock: IBM","theoretical:  0.648436267<br />sample:  0.7516548552<br />change:  7.516549e-01<br />stock: IBM","theoretical:  0.649778760<br />sample:  0.7518785569<br />change:  7.518786e-01<br />stock: IBM","theoretical:  0.651122424<br />sample:  0.7522864586<br />change:  7.522865e-01<br />stock: IBM","theoretical:  0.652467266<br />sample:  0.7525469150<br />change:  7.525469e-01<br />stock: IBM","theoretical:  0.653813289<br />sample:  0.7534653468<br />change:  7.534653e-01<br />stock: IBM","theoretical:  0.655160497<br 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0.7670343699<br />change:  7.670344e-01<br />stock: IBM","theoretical:  0.670059350<br />sample:  0.7687172503<br />change:  7.687173e-01<br />stock: IBM","theoretical:  0.671421146<br />sample:  0.7712370309<br />change:  7.712370e-01<br />stock: IBM","theoretical:  0.672784188<br />sample:  0.7712750154<br />change:  7.712750e-01<br />stock: IBM","theoretical:  0.674148481<br />sample:  0.7721660314<br />change:  7.721660e-01<br />stock: IBM","theoretical:  0.675514030<br />sample:  0.7744494073<br />change:  7.744494e-01<br />stock: IBM","theoretical:  0.676880840<br />sample:  0.7768683068<br />change:  7.768683e-01<br />stock: IBM","theoretical:  0.678248915<br />sample:  0.7793730407<br />change:  7.793730e-01<br />stock: IBM","theoretical:  0.679618261<br />sample:  0.7807363488<br />change:  7.807363e-01<br />stock: IBM","theoretical:  0.680988883<br />sample:  0.7928257093<br />change:  7.928257e-01<br />stock: IBM","theoretical:  0.682360785<br />sample:  0.7928999377<br />change:  7.928999e-01<br />stock: IBM","theoretical:  0.683733972<br />sample:  0.7935634974<br />change:  7.935635e-01<br />stock: IBM","theoretical:  0.685108451<br />sample:  0.7954883779<br />change:  7.954884e-01<br />stock: IBM","theoretical:  0.686484224<br />sample:  0.7963477883<br />change:  7.963478e-01<br />stock: IBM","theoretical:  0.687861298<br />sample:  0.7967051293<br />change:  7.967051e-01<br />stock: IBM","theoretical:  0.689239678<br />sample:  0.7978414830<br />change:  7.978415e-01<br />stock: IBM","theoretical:  0.690619369<br />sample:  0.7986593237<br />change:  7.986593e-01<br />stock: IBM","theoretical:  0.692000375<br />sample:  0.7991171472<br />change:  7.991171e-01<br />stock: IBM","theoretical:  0.693382703<br />sample:  0.8002722504<br />change:  8.002723e-01<br />stock: IBM","theoretical:  0.694766357<br />sample:  0.8050183040<br />change:  8.050183e-01<br />stock: IBM","theoretical:  0.696151342<br />sample:  0.8100029704<br />change:  8.100030e-01<br />stock: IBM","theoretical:  0.697537663<br />sample:  0.8112928540<br />change:  8.112929e-01<br />stock: IBM","theoretical:  0.698925327<br />sample:  0.8139734420<br />change:  8.139734e-01<br />stock: IBM","theoretical:  0.700314338<br />sample:  0.8155354231<br />change:  8.155354e-01<br />stock: IBM","theoretical:  0.701704701<br />sample:  0.8158261371<br />change:  8.158261e-01<br />stock: IBM","theoretical:  0.703096422<br />sample:  0.8202685719<br />change:  8.202686e-01<br />stock: IBM","theoretical:  0.704489507<br />sample:  0.8252769190<br />change:  8.252769e-01<br />stock: IBM","theoretical:  0.705883959<br />sample:  0.8270960651<br />change:  8.270961e-01<br />stock: IBM","theoretical:  0.707279786<br />sample:  0.8278915917<br />change:  8.278916e-01<br />stock: IBM","theoretical:  0.708676992<br />sample:  0.8314829346<br />change:  8.314829e-01<br />stock: IBM","theoretical:  0.710075583<br />sample:  0.8359857245<br />change:  8.359857e-01<br 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IBM","theoretical:  0.725553073<br />sample:  0.8577041057<br />change:  8.577041e-01<br />stock: IBM","theoretical:  0.726968718<br />sample:  0.8606105632<br />change:  8.606106e-01<br />stock: IBM","theoretical:  0.728385821<br />sample:  0.8616468065<br />change:  8.616468e-01<br />stock: IBM","theoretical:  0.729804389<br />sample:  0.8693362478<br />change:  8.693362e-01<br />stock: IBM","theoretical:  0.731224427<br />sample:  0.8716065238<br />change:  8.716065e-01<br />stock: IBM","theoretical:  0.732645941<br />sample:  0.8731153589<br />change:  8.731154e-01<br />stock: IBM","theoretical:  0.734068937<br />sample:  0.8736402700<br />change:  8.736403e-01<br />stock: IBM","theoretical:  0.735493421<br />sample:  0.8747372082<br />change:  8.747372e-01<br />stock: IBM","theoretical:  0.736919398<br />sample:  0.8757761675<br />change:  8.757762e-01<br />stock: IBM","theoretical:  0.738346876<br />sample:  0.8761631824<br />change:  8.761632e-01<br />stock: IBM","theoretical:  0.739775860<br />sample:  0.8783826797<br />change:  8.783827e-01<br />stock: IBM","theoretical:  0.741206357<br />sample:  0.8804092367<br />change:  8.804092e-01<br />stock: IBM","theoretical:  0.742638371<br />sample:  0.8804929753<br />change:  8.804930e-01<br />stock: IBM","theoretical:  0.744071911<br />sample:  0.8805727769<br />change:  8.805728e-01<br />stock: IBM","theoretical:  0.745506980<br />sample:  0.8814426875<br />change:  8.814427e-01<br />stock: IBM","theoretical:  0.746943587<br />sample:  0.8816657549<br />change:  8.816658e-01<br />stock: IBM","theoretical:  0.748381737<br />sample:  0.8830375399<br />change:  8.830375e-01<br />stock: IBM","theoretical:  0.749821437<br />sample:  0.8837321842<br />change:  8.837322e-01<br />stock: IBM","theoretical:  0.751262692<br />sample:  0.8877005624<br />change:  8.877006e-01<br />stock: IBM","theoretical:  0.752705510<br />sample:  0.8892718866<br />change:  8.892719e-01<br />stock: IBM","theoretical:  0.754149896<br />sample:  0.8897964763<br />change:  8.897965e-01<br />stock: IBM","theoretical:  0.755595858<br />sample:  0.8926593100<br />change:  8.926593e-01<br />stock: IBM","theoretical:  0.757043401<br />sample:  0.8935613320<br />change:  8.935613e-01<br />stock: IBM","theoretical:  0.758492532<br />sample:  0.8957563933<br />change:  8.957564e-01<br />stock: IBM","theoretical:  0.759943257<br />sample:  0.8971281927<br />change:  8.971282e-01<br />stock: IBM","theoretical:  0.761395584<br />sample:  0.9011785287<br />change:  9.011785e-01<br />stock: IBM","theoretical:  0.762849518<br />sample:  0.9013006721<br />change:  9.013007e-01<br />stock: IBM","theoretical:  0.764305067<br />sample:  0.9029965162<br />change:  9.029965e-01<br />stock: IBM","theoretical:  0.765762237<br />sample:  0.9060746361<br />change:  9.060746e-01<br />stock: IBM","theoretical:  0.767221035<br />sample:  0.9062002163<br />change:  9.062002e-01<br />stock: IBM","theoretical:  0.768681467<br />sample:  0.9069837620<br />change:  9.069838e-01<br />stock: IBM","theoretical:  0.770143541<br />sample:  0.9071784653<br />change:  9.071785e-01<br />stock: IBM","theoretical:  0.771607262<br />sample:  0.9087357676<br />change:  9.087358e-01<br />stock: IBM","theoretical:  0.773072639<br />sample:  0.9100536834<br />change:  9.100537e-01<br />stock: IBM","theoretical:  0.774539678<br />sample:  0.9124158625<br />change:  9.124159e-01<br />stock: IBM","theoretical:  0.776008386<br />sample:  0.9138383968<br />change:  9.138384e-01<br />stock: IBM","theoretical:  0.777478769<br />sample:  0.9140551541<br />change:  9.140552e-01<br />stock: IBM","theoretical:  0.778950835<br />sample:  0.9183830767<br />change:  9.183831e-01<br />stock: IBM","theoretical:  0.780424591<br />sample:  0.9203847149<br />change:  9.203847e-01<br />stock: IBM","theoretical:  0.781900044<br />sample:  0.9258280092<br />change:  9.258280e-01<br />stock: IBM","theoretical:  0.783377202<br />sample:  0.9264411644<br />change:  9.264412e-01<br />stock: IBM","theoretical:  0.784856070<br />sample:  0.9271973585<br />change:  9.271974e-01<br />stock: IBM","theoretical:  0.786336658<br />sample:  0.9289212802<br />change:  9.289213e-01<br />stock: IBM","theoretical:  0.787818970<br />sample:  0.9305402309<br />change:  9.305402e-01<br />stock: IBM","theoretical:  0.789303016<br />sample:  0.9322893991<br />change:  9.322894e-01<br />stock: IBM","theoretical:  0.790788803<br />sample:  0.9347750442<br />change:  9.347750e-01<br />stock: IBM","theoretical:  0.792276337<br />sample:  0.9357433924<br />change:  9.357434e-01<br />stock: IBM","theoretical:  0.793765626<br />sample:  0.9362152894<br />change:  9.362153e-01<br />stock: IBM","theoretical:  0.795256678<br />sample:  0.9362765052<br />change:  9.362765e-01<br />stock: IBM","theoretical:  0.796749500<br />sample:  0.9392265012<br />change:  9.392265e-01<br />stock: IBM","theoretical:  0.798244100<br />sample:  0.9392419757<br />change:  9.392420e-01<br />stock: IBM","theoretical:  0.799740485<br />sample:  0.9399943968<br />change:  9.399944e-01<br />stock: IBM","theoretical:  0.801238663<br />sample:  0.9408245916<br />change:  9.408246e-01<br />stock: IBM","theoretical:  0.802738641<br />sample:  0.9416268434<br />change:  9.416268e-01<br />stock: IBM","theoretical:  0.804240428<br />sample:  0.9499536071<br />change:  9.499536e-01<br />stock: IBM","theoretical:  0.805744031<br />sample:  0.9510171385<br />change:  9.510171e-01<br />stock: IBM","theoretical:  0.807249458<br />sample:  0.9511525007<br />change:  9.511525e-01<br />stock: IBM","theoretical:  0.808756716<br />sample:  0.9513108600<br />change:  9.513109e-01<br />stock: IBM","theoretical:  0.810265814<br />sample:  0.9517503010<br />change:  9.517503e-01<br />stock: IBM","theoretical:  0.811776760<br />sample:  0.9532386298<br />change:  9.532386e-01<br />stock: IBM","theoretical:  0.813289561<br />sample:  0.9535353406<br />change:  9.535353e-01<br />stock: IBM","theoretical:  0.814804226<br />sample:  0.9556876509<br />change:  9.556877e-01<br />stock: IBM","theoretical:  0.816320762<br />sample:  0.9573143957<br />change:  9.573144e-01<br />stock: IBM","theoretical:  0.817839178<br />sample:  0.9597662426<br />change:  9.597662e-01<br />stock: IBM","theoretical:  0.819359482<br />sample:  0.9629611429<br />change:  9.629611e-01<br />stock: IBM","theoretical:  0.820881682<br />sample:  0.9630789672<br />change:  9.630790e-01<br />stock: IBM","theoretical:  0.822405787<br />sample:  0.9683537847<br />change:  9.683538e-01<br />stock: IBM","theoretical:  0.823931804<br />sample:  0.9690835437<br />change:  9.690835e-01<br />stock: IBM","theoretical:  0.825459743<br />sample:  0.9699628046<br />change:  9.699628e-01<br />stock: IBM","theoretical:  0.826989611<br />sample:  0.9707903413<br />change:  9.707903e-01<br />stock: IBM","theoretical:  0.828521417<br />sample:  0.9712183556<br />change:  9.712184e-01<br />stock: IBM","theoretical:  0.830055169<br />sample:  0.9712561351<br />change:  9.712561e-01<br />stock: IBM","theoretical:  0.831590877<br />sample:  0.9713727341<br />change:  9.713727e-01<br />stock: IBM","theoretical:  0.833128549<br />sample:  0.9726086673<br />change:  9.726087e-01<br />stock: IBM","theoretical:  0.834668192<br />sample:  0.9760636880<br />change:  9.760637e-01<br />stock: IBM","theoretical:  0.836209817<br />sample:  0.9766833888<br />change:  9.766834e-01<br />stock: IBM","theoretical:  0.837753432<br />sample:  0.9773364090<br />change:  9.773364e-01<br />stock: IBM","theoretical:  0.839299046<br />sample:  0.9774379412<br />change:  9.774379e-01<br />stock: IBM","theoretical:  0.840846667<br />sample:  0.9789196840<br />change:  9.789197e-01<br />stock: IBM","theoretical:  0.842396305<br />sample:  0.9827152886<br />change:  9.827153e-01<br />stock: IBM","theoretical:  0.843947969<br />sample:  0.9873725571<br />change:  9.873726e-01<br />stock: IBM","theoretical:  0.845501667<br />sample:  0.9883543656<br />change:  9.883544e-01<br />stock: IBM","theoretical:  0.847057408<br />sample:  0.9893624485<br />change:  9.893624e-01<br />stock: IBM","theoretical:  0.848615203<br />sample:  0.9907656253<br />change:  9.907656e-01<br />stock: IBM","theoretical:  0.850175059<br />sample:  0.9909607213<br />change:  9.909607e-01<br />stock: IBM","theoretical:  0.851736987<br />sample:  0.9914503277<br />change:  9.914503e-01<br />stock: IBM","theoretical:  0.853300996<br />sample:  0.9919388558<br />change:  9.919389e-01<br />stock: IBM","theoretical:  0.854867095<br />sample:  0.9920828391<br />change:  9.920828e-01<br />stock: IBM","theoretical:  0.856435293<br />sample:  0.9936331503<br />change:  9.936332e-01<br />stock: IBM","theoretical:  0.858005600<br />sample:  0.9949466146<br />change:  9.949466e-01<br />stock: IBM","theoretical:  0.859578026<br />sample:  1.0010947536<br />change:  1.001095e+00<br />stock: IBM","theoretical:  0.861152580<br />sample:  1.0013599894<br />change:  1.001360e+00<br />stock: IBM","theoretical:  0.862729272<br />sample:  1.0034758313<br />change:  1.003476e+00<br />stock: IBM","theoretical:  0.864308112<br />sample:  1.0038864132<br />change:  1.003886e+00<br />stock: IBM","theoretical:  0.865889109<br />sample:  1.0048382205<br />change:  1.004838e+00<br />stock: IBM","theoretical:  0.867472273<br />sample:  1.0059672772<br />change:  1.005967e+00<br />stock: IBM","theoretical:  0.869057615<br />sample:  1.0078468603<br />change:  1.007847e+00<br />stock: IBM","theoretical:  0.870645144<br />sample:  1.0097203985<br />change:  1.009720e+00<br />stock: IBM","theoretical:  0.872234870<br />sample:  1.0106160648<br />change:  1.010616e+00<br />stock: IBM","theoretical:  0.873826803<br />sample:  1.0106913449<br />change:  1.010691e+00<br />stock: IBM","theoretical:  0.875420954<br />sample:  1.0122130673<br />change:  1.012213e+00<br />stock: IBM","theoretical:  0.877017333<br />sample:  1.0143628026<br />change:  1.014363e+00<br />stock: IBM","theoretical:  0.878615950<br />sample:  1.0173812101<br />change:  1.017381e+00<br />stock: IBM","theoretical:  0.880216816<br />sample:  1.0199862523<br />change:  1.019986e+00<br />stock: IBM","theoretical:  0.881819940<br />sample:  1.0264224578<br />change:  1.026422e+00<br />stock: IBM","theoretical:  0.883425335<br />sample:  1.0269662626<br />change:  1.026966e+00<br />stock: IBM","theoretical:  0.885033009<br />sample:  1.0273992244<br />change:  1.027399e+00<br />stock: IBM","theoretical:  0.886642974<br />sample:  1.0279733824<br />change:  1.027973e+00<br />stock: IBM","theoretical:  0.888255240<br />sample:  1.0314978445<br />change:  1.031498e+00<br />stock: IBM","theoretical:  0.889869818<br />sample:  1.0357030570<br />change:  1.035703e+00<br />stock: IBM","theoretical:  0.891486720<br />sample:  1.0357330800<br />change:  1.035733e+00<br />stock: IBM","theoretical:  0.893105956<br />sample:  1.0390432474<br />change:  1.039043e+00<br />stock: IBM","theoretical:  0.894727537<br />sample:  1.0395803733<br />change:  1.039580e+00<br />stock: IBM","theoretical:  0.896351473<br />sample:  1.0415021904<br />change:  1.041502e+00<br />stock: IBM","theoretical:  0.897977778<br />sample:  1.0416684501<br />change:  1.041668e+00<br />stock: IBM","theoretical:  0.899606460<br />sample:  1.0441391531<br />change:  1.044139e+00<br />stock: IBM","theoretical:  0.901237533<br />sample:  1.0442070808<br />change:  1.044207e+00<br />stock: IBM","theoretical:  0.902871006<br />sample:  1.0470859049<br />change:  1.047086e+00<br />stock: IBM","theoretical:  0.904506893<br />sample:  1.0474803136<br />change:  1.047480e+00<br />stock: IBM","theoretical:  0.906145203<br />sample:  1.0481511019<br />change:  1.048151e+00<br />stock: IBM","theoretical:  0.907785949<br />sample:  1.0508025587<br />change:  1.050803e+00<br />stock: IBM","theoretical:  0.909429143<br />sample:  1.0539145016<br />change:  1.053915e+00<br />stock: IBM","theoretical:  0.911074796<br />sample:  1.0540758575<br />change:  1.054076e+00<br />stock: IBM","theoretical:  0.912722920<br />sample:  1.0552779439<br />change:  1.055278e+00<br />stock: IBM","theoretical:  0.914373527<br />sample:  1.0558500573<br />change:  1.055850e+00<br />stock: IBM","theoretical:  0.916026629<br />sample:  1.0566743650<br />change:  1.056674e+00<br />stock: IBM","theoretical:  0.917682238<br />sample:  1.0577453667<br />change:  1.057745e+00<br />stock: IBM","theoretical:  0.919340366<br />sample:  1.0596898598<br />change:  1.059690e+00<br />stock: IBM","theoretical:  0.921001026<br />sample:  1.0621225030<br />change:  1.062123e+00<br />stock: IBM","theoretical:  0.922664229<br />sample:  1.0653972334<br />change:  1.065397e+00<br />stock: IBM","theoretical:  0.924329989<br />sample:  1.0661183352<br />change:  1.066118e+00<br />stock: IBM","theoretical:  0.925998317<br />sample:  1.0668645253<br />change:  1.066865e+00<br />stock: IBM","theoretical:  0.927669227<br />sample:  1.0673745317<br />change:  1.067375e+00<br />stock: IBM","theoretical:  0.929342731<br />sample:  1.0687654702<br />change:  1.068765e+00<br />stock: IBM","theoretical:  0.931018842<br />sample:  1.0691085989<br />change:  1.069109e+00<br />stock: IBM","theoretical:  0.932697572<br />sample:  1.0691887606<br />change:  1.069189e+00<br />stock: IBM","theoretical:  0.934378935<br />sample:  1.0699487968<br />change:  1.069949e+00<br />stock: IBM","theoretical:  0.936062943<br />sample:  1.0710870195<br />change:  1.071087e+00<br />stock: IBM","theoretical:  0.937749611<br />sample:  1.0711522112<br />change:  1.071152e+00<br />stock: IBM","theoretical:  0.939438950<br />sample:  1.0724734360<br />change:  1.072473e+00<br />stock: IBM","theoretical:  0.941130975<br />sample:  1.0744105225<br />change:  1.074411e+00<br />stock: IBM","theoretical:  0.942825698<br />sample:  1.0757354043<br />change:  1.075735e+00<br />stock: IBM","theoretical:  0.944523133<br />sample:  1.0861005586<br />change:  1.086101e+00<br />stock: IBM","theoretical:  0.946223295<br />sample:  1.0869521191<br />change:  1.086952e+00<br />stock: IBM","theoretical:  0.947926195<br />sample:  1.0880950463<br />change:  1.088095e+00<br />stock: IBM","theoretical:  0.949631850<br />sample:  1.0886137633<br />change:  1.088614e+00<br />stock: IBM","theoretical:  0.951340271<br />sample:  1.0912385853<br />change:  1.091239e+00<br />stock: IBM","theoretical:  0.953051473<br />sample:  1.0947104059<br />change:  1.094710e+00<br />stock: IBM","theoretical:  0.954765471<br />sample:  1.0948661765<br />change:  1.094866e+00<br />stock: IBM","theoretical:  0.956482279<br />sample:  1.0991562412<br />change:  1.099156e+00<br />stock: IBM","theoretical:  0.958201910<br />sample:  1.1004012698<br />change:  1.100401e+00<br />stock: IBM","theoretical:  0.959924379<br />sample:  1.1016555017<br />change:  1.101656e+00<br />stock: IBM","theoretical:  0.961649701<br />sample:  1.1031083580<br />change:  1.103108e+00<br />stock: IBM","theoretical:  0.963377890<br />sample:  1.1034466192<br />change:  1.103447e+00<br />stock: IBM","theoretical:  0.965108962<br />sample:  1.1039986465<br />change:  1.103999e+00<br />stock: IBM","theoretical:  0.966842930<br />sample:  1.1088422269<br />change:  1.108842e+00<br />stock: IBM","theoretical:  0.968579811<br />sample:  1.1090978023<br />change:  1.109098e+00<br />stock: IBM","theoretical:  0.970319618<br />sample:  1.1107932676<br />change:  1.110793e+00<br />stock: IBM","theoretical:  0.972062367<br />sample:  1.1116849988<br />change:  1.111685e+00<br />stock: IBM","theoretical:  0.973808073<br />sample:  1.1144678267<br />change:  1.114468e+00<br />stock: IBM","theoretical:  0.975556752<br />sample:  1.1157870131<br />change:  1.115787e+00<br />stock: IBM","theoretical:  0.977308420<br />sample:  1.1168346797<br />change:  1.116835e+00<br />stock: IBM","theoretical:  0.979063091<br />sample:  1.1179230912<br />change:  1.117923e+00<br />stock: IBM","theoretical:  0.980820782<br />sample:  1.1182349185<br />change:  1.118235e+00<br />stock: IBM","theoretical:  0.982581508<br />sample:  1.1185260702<br />change:  1.118526e+00<br />stock: IBM","theoretical:  0.984345286<br />sample:  1.1209750481<br />change:  1.120975e+00<br />stock: IBM","theoretical:  0.986112132<br />sample:  1.1236501642<br />change:  1.123650e+00<br />stock: IBM","theoretical:  0.987882061<br />sample:  1.1250469302<br />change:  1.125047e+00<br />stock: IBM","theoretical:  0.989655090<br />sample:  1.1275429028<br />change:  1.127543e+00<br />stock: IBM","theoretical:  0.991431236<br />sample:  1.1275742888<br />change:  1.127574e+00<br />stock: IBM","theoretical:  0.993210515<br />sample:  1.1325675774<br />change:  1.132568e+00<br />stock: IBM","theoretical:  0.994992944<br />sample:  1.1338704839<br />change:  1.133870e+00<br />stock: IBM","theoretical:  0.996778539<br />sample:  1.1372755289<br />change:  1.137276e+00<br />stock: IBM","theoretical:  0.998567319<br />sample:  1.1427774195<br />change:  1.142777e+00<br />stock: IBM","theoretical:  1.000359299<br />sample:  1.1441448812<br />change:  1.144145e+00<br />stock: IBM","theoretical:  1.002154497<br />sample:  1.1451555856<br />change:  1.145156e+00<br />stock: IBM","theoretical:  1.003952931<br />sample:  1.1482413799<br />change:  1.148241e+00<br />stock: IBM","theoretical:  1.005754618<br />sample:  1.1486509920<br />change:  1.148651e+00<br />stock: IBM","theoretical:  1.007559576<br />sample:  1.1545198286<br />change:  1.154520e+00<br />stock: IBM","theoretical:  1.009367822<br />sample:  1.1549175024<br />change:  1.154918e+00<br />stock: IBM","theoretical:  1.011179374<br />sample:  1.1555069007<br />change:  1.155507e+00<br />stock: IBM","theoretical:  1.012994251<br />sample:  1.1625393943<br />change:  1.162539e+00<br />stock: IBM","theoretical:  1.014812471<br />sample:  1.1673779105<br />change:  1.167378e+00<br />stock: IBM","theoretical:  1.016634052<br />sample:  1.1684264785<br />change:  1.168426e+00<br />stock: IBM","theoretical:  1.018459013<br />sample:  1.1715311691<br />change:  1.171531e+00<br />stock: IBM","theoretical:  1.020287371<br />sample:  1.1724840672<br />change:  1.172484e+00<br />stock: IBM","theoretical:  1.022119147<br />sample:  1.1739360283<br />change:  1.173936e+00<br />stock: IBM","theoretical:  1.023954359<br />sample:  1.1761003590<br />change:  1.176100e+00<br />stock: IBM","theoretical:  1.025793026<br />sample:  1.1784095163<br />change:  1.178410e+00<br />stock: IBM","theoretical:  1.027635168<br />sample:  1.1785636548<br />change:  1.178564e+00<br />stock: IBM","theoretical:  1.029480803<br />sample:  1.1830103869<br />change:  1.183010e+00<br />stock: IBM","theoretical:  1.031329952<br />sample:  1.1831152833<br />change:  1.183115e+00<br />stock: IBM","theoretical:  1.033182634<br />sample:  1.1832641481<br />change:  1.183264e+00<br />stock: IBM","theoretical:  1.035038869<br />sample:  1.1841126749<br />change:  1.184113e+00<br />stock: IBM","theoretical:  1.036898678<br />sample:  1.1859640335<br />change:  1.185964e+00<br />stock: IBM","theoretical:  1.038762080<br />sample:  1.1860836587<br />change:  1.186084e+00<br />stock: IBM","theoretical:  1.040629095<br />sample:  1.1886430363<br />change:  1.188643e+00<br />stock: IBM","theoretical:  1.042499746<br />sample:  1.1894162499<br />change:  1.189416e+00<br />stock: IBM","theoretical:  1.044374051<br />sample:  1.1902746595<br />change:  1.190275e+00<br />stock: IBM","theoretical:  1.046252032<br />sample:  1.1924466477<br />change:  1.192447e+00<br />stock: IBM","theoretical:  1.048133711<br />sample:  1.1926892022<br />change:  1.192689e+00<br />stock: IBM","theoretical:  1.050019108<br />sample:  1.1940269712<br />change:  1.194027e+00<br />stock: IBM","theoretical:  1.051908245<br />sample:  1.1970037160<br />change:  1.197004e+00<br />stock: IBM","theoretical:  1.053801144<br />sample:  1.2075082635<br />change:  1.207508e+00<br />stock: IBM","theoretical:  1.055697826<br />sample:  1.2155213760<br />change:  1.215521e+00<br />stock: IBM","theoretical:  1.057598314<br />sample:  1.2201266401<br />change:  1.220127e+00<br />stock: IBM","theoretical:  1.059502629<br />sample:  1.2206412898<br />change:  1.220641e+00<br />stock: IBM","theoretical:  1.061410794<br />sample:  1.2248259153<br />change:  1.224826e+00<br />stock: IBM","theoretical:  1.063322831<br />sample:  1.2276361986<br />change:  1.227636e+00<br />stock: IBM","theoretical:  1.065238764<br />sample:  1.2288739714<br />change:  1.228874e+00<br />stock: IBM","theoretical:  1.067158615<br />sample:  1.2289666114<br />change:  1.228967e+00<br />stock: IBM","theoretical:  1.069082408<br />sample:  1.2298399126<br />change:  1.229840e+00<br />stock: IBM","theoretical:  1.071010165<br />sample:  1.2357463845<br />change:  1.235746e+00<br />stock: IBM","theoretical:  1.072941911<br />sample:  1.2418825657<br />change:  1.241883e+00<br />stock: IBM","theoretical:  1.074877669<br />sample:  1.2475410649<br />change:  1.247541e+00<br />stock: IBM","theoretical:  1.076817463<br />sample:  1.2512284158<br />change:  1.251228e+00<br />stock: IBM","theoretical:  1.078761317<br />sample:  1.2539398501<br />change:  1.253940e+00<br />stock: IBM","theoretical:  1.080709257<br />sample:  1.2542575990<br />change:  1.254258e+00<br />stock: IBM","theoretical:  1.082661305<br />sample:  1.2547888521<br />change:  1.254789e+00<br />stock: IBM","theoretical:  1.084617488<br />sample:  1.2562130893<br />change:  1.256213e+00<br />stock: IBM","theoretical:  1.086577830<br />sample:  1.2580574694<br />change:  1.258057e+00<br />stock: IBM","theoretical:  1.088542357<br />sample:  1.2584122074<br />change:  1.258412e+00<br />stock: IBM","theoretical:  1.090511093<br />sample:  1.2620026393<br />change:  1.262003e+00<br />stock: IBM","theoretical:  1.092484066<br />sample:  1.2639665353<br />change:  1.263967e+00<br />stock: IBM","theoretical:  1.094461300<br />sample:  1.2642437317<br />change:  1.264244e+00<br />stock: IBM","theoretical:  1.096442823<br />sample:  1.2647194144<br />change:  1.264719e+00<br />stock: IBM","theoretical:  1.098428659<br />sample:  1.2657261120<br />change:  1.265726e+00<br />stock: IBM","theoretical:  1.100418837<br />sample:  1.2710391695<br />change:  1.271039e+00<br />stock: IBM","theoretical:  1.102413384<br />sample:  1.2734524989<br />change:  1.273452e+00<br />stock: IBM","theoretical:  1.104412325<br />sample:  1.2773400853<br />change:  1.277340e+00<br />stock: IBM","theoretical:  1.106415689<br />sample:  1.2801181940<br />change:  1.280118e+00<br />stock: IBM","theoretical:  1.108423504<br />sample:  1.2854568662<br />change:  1.285457e+00<br />stock: IBM","theoretical:  1.110435797<br />sample:  1.2871102915<br />change:  1.287110e+00<br />stock: IBM","theoretical:  1.112452597<br />sample:  1.2892605941<br />change:  1.289261e+00<br />stock: IBM","theoretical:  1.114473931<br />sample:  1.2899628709<br />change:  1.289963e+00<br />stock: IBM","theoretical:  1.116499830<br />sample:  1.2907693416<br />change:  1.290769e+00<br />stock: IBM","theoretical:  1.118530321<br />sample:  1.2945143780<br />change:  1.294514e+00<br />stock: IBM","theoretical:  1.120565435<br />sample:  1.2956282813<br />change:  1.295628e+00<br />stock: IBM","theoretical:  1.122605200<br />sample:  1.2996717151<br />change:  1.299672e+00<br />stock: IBM","theoretical:  1.124649646<br />sample:  1.3085583402<br />change:  1.308558e+00<br />stock: IBM","theoretical:  1.126698804<br />sample:  1.3093784133<br />change:  1.309378e+00<br />stock: IBM","theoretical:  1.128752704<br />sample:  1.3099773499<br />change:  1.309977e+00<br />stock: IBM","theoretical:  1.130811377<br />sample:  1.3129809879<br />change:  1.312981e+00<br />stock: IBM","theoretical:  1.132874854<br />sample:  1.3153206394<br />change:  1.315321e+00<br />stock: IBM","theoretical:  1.134943166<br />sample:  1.3160746793<br />change:  1.316075e+00<br />stock: IBM","theoretical:  1.137016344<br />sample:  1.3167601003<br />change:  1.316760e+00<br />stock: IBM","theoretical:  1.139094421<br />sample:  1.3181799547<br />change:  1.318180e+00<br />stock: IBM","theoretical:  1.141177428<br />sample:  1.3217896534<br />change:  1.321790e+00<br />stock: IBM","theoretical:  1.143265399<br />sample:  1.3220460386<br />change:  1.322046e+00<br />stock: IBM","theoretical:  1.145358366<br />sample:  1.3265270994<br />change:  1.326527e+00<br />stock: IBM","theoretical:  1.147456362<br />sample:  1.3287444834<br />change:  1.328744e+00<br />stock: IBM","theoretical:  1.149559421<br />sample:  1.3301704095<br />change:  1.330170e+00<br />stock: IBM","theoretical:  1.151667577<br />sample:  1.3324436160<br />change:  1.332444e+00<br />stock: IBM","theoretical:  1.153780863<br />sample:  1.3326108370<br />change:  1.332611e+00<br />stock: IBM","theoretical:  1.155899315<br />sample:  1.3340990443<br />change:  1.334099e+00<br />stock: IBM","theoretical:  1.158022968<br />sample:  1.3361162742<br />change:  1.336116e+00<br />stock: IBM","theoretical:  1.160151855<br />sample:  1.3371656450<br />change:  1.337166e+00<br />stock: IBM","theoretical:  1.162286014<br />sample:  1.3385106445<br />change:  1.338511e+00<br />stock: IBM","theoretical:  1.164425479<br />sample:  1.3468339602<br />change:  1.346834e+00<br />stock: IBM","theoretical:  1.166570288<br />sample:  1.3525549578<br />change:  1.352555e+00<br />stock: IBM","theoretical:  1.168720477<br />sample:  1.3564584649<br />change:  1.356458e+00<br />stock: IBM","theoretical:  1.170876083<br />sample:  1.3632284130<br />change:  1.363228e+00<br />stock: IBM","theoretical:  1.173037143<br />sample:  1.3658017394<br />change:  1.365802e+00<br />stock: IBM","theoretical:  1.175203696<br />sample:  1.3674757113<br />change:  1.367476e+00<br />stock: IBM","theoretical:  1.177375778<br />sample:  1.3683513198<br />change:  1.368351e+00<br />stock: IBM","theoretical:  1.179553430<br />sample:  1.3746734462<br />change:  1.374673e+00<br />stock: IBM","theoretical:  1.181736690<br />sample:  1.3792461420<br />change:  1.379246e+00<br />stock: IBM","theoretical:  1.183925598<br />sample:  1.3819203236<br />change:  1.381920e+00<br />stock: IBM","theoretical:  1.186120192<br />sample:  1.3825547261<br />change:  1.382555e+00<br />stock: IBM","theoretical:  1.188320515<br />sample:  1.3830844153<br />change:  1.383084e+00<br />stock: IBM","theoretical:  1.190526605<br />sample:  1.3833109637<br />change:  1.383311e+00<br />stock: IBM","theoretical:  1.192738505<br />sample:  1.3886152993<br />change:  1.388615e+00<br />stock: IBM","theoretical:  1.194956256<br />sample:  1.3893023167<br />change:  1.389302e+00<br />stock: IBM","theoretical:  1.197179900<br />sample:  1.3894591928<br />change:  1.389459e+00<br />stock: IBM","theoretical:  1.199409479<br />sample:  1.3905454215<br />change:  1.390545e+00<br />stock: IBM","theoretical:  1.201645037<br />sample:  1.3916170267<br />change:  1.391617e+00<br />stock: IBM","theoretical:  1.203886616<br />sample:  1.4044918919<br />change:  1.404492e+00<br />stock: IBM","theoretical:  1.206134260<br />sample:  1.4066972638<br />change:  1.406697e+00<br />stock: IBM","theoretical:  1.208388015<br />sample:  1.4152143085<br />change:  1.415214e+00<br />stock: IBM","theoretical:  1.210647924<br />sample:  1.4171448772<br />change:  1.417145e+00<br />stock: IBM","theoretical:  1.212914033<br />sample:  1.4238105206<br />change:  1.423811e+00<br />stock: IBM","theoretical:  1.215186388<br />sample:  1.4258439469<br />change:  1.425844e+00<br />stock: IBM","theoretical:  1.217465035<br />sample:  1.4292308872<br />change:  1.429231e+00<br />stock: IBM","theoretical:  1.219750021<br />sample:  1.4321796241<br />change:  1.432180e+00<br />stock: IBM","theoretical:  1.222041393<br />sample:  1.4340095979<br />change:  1.434010e+00<br />stock: IBM","theoretical:  1.224339200<br />sample:  1.4348746892<br />change:  1.434875e+00<br />stock: IBM","theoretical:  1.226643489<br />sample:  1.4451834422<br />change:  1.445183e+00<br />stock: IBM","theoretical:  1.228954310<br />sample:  1.4478598597<br />change:  1.447860e+00<br />stock: IBM","theoretical:  1.231271712<br />sample:  1.4547926321<br />change:  1.454793e+00<br />stock: IBM","theoretical:  1.233595745<br />sample:  1.4555305309<br />change:  1.455531e+00<br />stock: IBM","theoretical:  1.235926461<br />sample:  1.4557746542<br />change:  1.455775e+00<br />stock: IBM","theoretical:  1.238263909<br />sample:  1.4591262929<br />change:  1.459126e+00<br />stock: IBM","theoretical:  1.240608143<br />sample:  1.4631792222<br />change:  1.463179e+00<br />stock: IBM","theoretical:  1.242959214<br />sample:  1.4656152464<br />change:  1.465615e+00<br />stock: IBM","theoretical:  1.245317176<br />sample:  1.4693967222<br />change:  1.469397e+00<br />stock: IBM","theoretical:  1.247682083<br />sample:  1.4770723979<br />change:  1.477072e+00<br />stock: IBM","theoretical:  1.250053987<br />sample:  1.4848997107<br />change:  1.484900e+00<br />stock: IBM","theoretical:  1.252432946<br />sample:  1.4876706139<br />change:  1.487671e+00<br />stock: IBM","theoretical:  1.254819014<br />sample:  1.4879021668<br />change:  1.487902e+00<br />stock: IBM","theoretical:  1.257212247<br />sample:  1.4886875310<br />change:  1.488688e+00<br />stock: IBM","theoretical:  1.259612703<br />sample:  1.4898360922<br />change:  1.489836e+00<br />stock: IBM","theoretical:  1.262020439<br />sample:  1.4922890673<br />change:  1.492289e+00<br />stock: IBM","theoretical:  1.264435514<br />sample:  1.4945443929<br />change:  1.494544e+00<br />stock: IBM","theoretical:  1.266857986<br />sample:  1.4950957085<br />change:  1.495096e+00<br />stock: IBM","theoretical:  1.269287916<br />sample:  1.5019860673<br />change:  1.501986e+00<br />stock: IBM","theoretical:  1.271725363<br />sample:  1.5057490057<br />change:  1.505749e+00<br />stock: IBM","theoretical:  1.274170389<br />sample:  1.5074287297<br />change:  1.507429e+00<br />stock: IBM","theoretical:  1.276623056<br />sample:  1.5103745658<br />change:  1.510375e+00<br />stock: IBM","theoretical:  1.279083427<br />sample:  1.5187662143<br />change:  1.518766e+00<br />stock: IBM","theoretical:  1.281551566<br />sample:  1.5191997225<br />change:  1.519200e+00<br />stock: IBM","theoretical:  1.284027535<br />sample:  1.5447915841<br />change:  1.544792e+00<br />stock: IBM","theoretical:  1.286511402<br />sample:  1.5554834433<br />change:  1.555483e+00<br />stock: IBM","theoretical:  1.289003232<br />sample:  1.5702039550<br />change:  1.570204e+00<br />stock: IBM","theoretical:  1.291503090<br />sample:  1.5761789072<br />change:  1.576179e+00<br />stock: IBM","theoretical:  1.294011047<br />sample:  1.5769183117<br />change:  1.576918e+00<br />stock: IBM","theoretical:  1.296527168<br />sample:  1.5773657768<br />change:  1.577366e+00<br />stock: IBM","theoretical:  1.299051525<br />sample:  1.5867063269<br />change:  1.586706e+00<br />stock: IBM","theoretical:  1.301584187<br />sample:  1.5882105784<br />change:  1.588211e+00<br />stock: IBM","theoretical:  1.304125225<br />sample:  1.5948431027<br />change:  1.594843e+00<br />stock: IBM","theoretical:  1.306674713<br />sample:  1.5971758278<br />change:  1.597176e+00<br />stock: IBM","theoretical:  1.309232721<br />sample:  1.6018892212<br />change:  1.601889e+00<br />stock: IBM","theoretical:  1.311799326<br />sample:  1.6056443292<br />change:  1.605644e+00<br />stock: IBM","theoretical:  1.314374601<br />sample:  1.6061022422<br />change:  1.606102e+00<br />stock: IBM","theoretical:  1.316958622<br />sample:  1.6165225263<br />change:  1.616523e+00<br />stock: IBM","theoretical:  1.319551468<br />sample:  1.6376770914<br />change:  1.637677e+00<br />stock: IBM","theoretical:  1.322153215<br />sample:  1.6396180281<br />change:  1.639618e+00<br />stock: IBM","theoretical:  1.324763942<br />sample:  1.6610672304<br />change:  1.661067e+00<br />stock: IBM","theoretical:  1.327383731<br />sample:  1.6612754268<br />change:  1.661275e+00<br />stock: IBM","theoretical:  1.330012661<br />sample:  1.6613588298<br />change:  1.661359e+00<br />stock: IBM","theoretical:  1.332650816<br />sample:  1.6626715458<br />change:  1.662672e+00<br />stock: IBM","theoretical:  1.335298278<br />sample:  1.6727369424<br />change:  1.672737e+00<br />stock: IBM","theoretical:  1.337955133<br />sample:  1.6816503984<br />change:  1.681650e+00<br />stock: IBM","theoretical:  1.340621467<br />sample:  1.6874394700<br />change:  1.687439e+00<br />stock: IBM","theoretical:  1.343297365<br />sample:  1.6976629545<br />change:  1.697663e+00<br />stock: IBM","theoretical:  1.345982917<br />sample:  1.6977834607<br />change:  1.697783e+00<br />stock: IBM","theoretical:  1.348678211<br />sample:  1.7022342471<br />change:  1.702234e+00<br />stock: IBM","theoretical:  1.351383339<br />sample:  1.7028594368<br />change:  1.702859e+00<br />stock: IBM","theoretical:  1.354098392<br />sample:  1.7041326662<br />change:  1.704133e+00<br />stock: IBM","theoretical:  1.356823464<br />sample:  1.7049847706<br />change:  1.704985e+00<br />stock: IBM","theoretical:  1.359558649<br />sample:  1.7099018859<br />change:  1.709902e+00<br />stock: IBM","theoretical:  1.362304043<br />sample:  1.7205304754<br />change:  1.720530e+00<br />stock: IBM","theoretical:  1.365059744<br />sample:  1.7213346943<br />change:  1.721335e+00<br />stock: IBM","theoretical:  1.367825850<br />sample:  1.7249127111<br />change:  1.724913e+00<br />stock: IBM","theoretical:  1.370602461<br />sample:  1.7270246087<br />change:  1.727025e+00<br />stock: IBM","theoretical:  1.373389680<br />sample:  1.7331504533<br />change:  1.733150e+00<br />stock: IBM","theoretical:  1.376187608<br />sample:  1.7429262992<br />change:  1.742926e+00<br />stock: IBM","theoretical:  1.378996352<br />sample:  1.7436331802<br />change:  1.743633e+00<br />stock: IBM","theoretical:  1.381816018<br />sample:  1.7523982450<br />change:  1.752398e+00<br />stock: IBM","theoretical:  1.384646712<br />sample:  1.7525410779<br />change:  1.752541e+00<br />stock: IBM","theoretical:  1.387488545<br />sample:  1.7547559058<br />change:  1.754756e+00<br />stock: IBM","theoretical:  1.390341628<br />sample:  1.7562101243<br />change:  1.756210e+00<br />stock: IBM","theoretical:  1.393206073<br />sample:  1.7636548623<br />change:  1.763655e+00<br />stock: IBM","theoretical:  1.396081996<br />sample:  1.7681840763<br />change:  1.768184e+00<br />stock: IBM","theoretical:  1.398969512<br />sample:  1.7741474945<br />change:  1.774147e+00<br />stock: IBM","theoretical:  1.401868740<br />sample:  1.7818882188<br />change:  1.781888e+00<br />stock: IBM","theoretical:  1.404779799<br />sample:  1.7850039622<br />change:  1.785004e+00<br />stock: IBM","theoretical:  1.407702812<br />sample:  1.7874699803<br />change:  1.787470e+00<br />stock: IBM","theoretical:  1.410637901<br />sample:  1.7902576875<br />change:  1.790258e+00<br />stock: IBM","theoretical:  1.413585194<br />sample:  1.7908636965<br />change:  1.790864e+00<br />stock: IBM","theoretical:  1.416544817<br />sample:  1.7933521490<br />change:  1.793352e+00<br />stock: IBM","theoretical:  1.419516901<br />sample:  1.8041713280<br />change:  1.804171e+00<br />stock: IBM","theoretical:  1.422501577<br />sample:  1.8107907392<br />change:  1.810791e+00<br />stock: IBM","theoretical:  1.425498978<br />sample:  1.8148841068<br />change:  1.814884e+00<br />stock: IBM","theoretical:  1.428509243<br />sample:  1.8157429136<br />change:  1.815743e+00<br />stock: IBM","theoretical:  1.431532507<br />sample:  1.8172959181<br />change:  1.817296e+00<br />stock: IBM","theoretical:  1.434568914<br />sample:  1.8185019910<br />change:  1.818502e+00<br />stock: IBM","theoretical:  1.437618604<br />sample:  1.8240666431<br />change:  1.824067e+00<br />stock: IBM","theoretical:  1.440681724<br />sample:  1.8241165362<br />change:  1.824117e+00<br />stock: IBM","theoretical:  1.443758422<br />sample:  1.8320389222<br />change:  1.832039e+00<br />stock: IBM","theoretical:  1.446848847<br />sample:  1.8337130636<br />change:  1.833713e+00<br />stock: IBM","theoretical:  1.449953153<br />sample:  1.8338895787<br />change:  1.833890e+00<br />stock: IBM","theoretical:  1.453071495<br />sample:  1.8368516474<br />change:  1.836852e+00<br />stock: IBM","theoretical:  1.456204031<br />sample:  1.8377580251<br />change:  1.837758e+00<br />stock: IBM","theoretical:  1.459350922<br />sample:  1.8380073174<br />change:  1.838007e+00<br />stock: IBM","theoretical:  1.462512331<br />sample:  1.8392313666<br />change:  1.839231e+00<br />stock: IBM","theoretical:  1.465688426<br />sample:  1.8424743199<br />change:  1.842474e+00<br />stock: IBM","theoretical:  1.468879375<br />sample:  1.8484690958<br />change:  1.848469e+00<br />stock: IBM","theoretical:  1.472085351<br />sample:  1.8509701083<br />change:  1.850970e+00<br />stock: IBM","theoretical:  1.475306529<br />sample:  1.8526658635<br />change:  1.852666e+00<br />stock: IBM","theoretical:  1.478543088<br />sample:  1.8531195427<br />change:  1.853120e+00<br />stock: IBM","theoretical:  1.481795210<br />sample:  1.8570880243<br />change:  1.857088e+00<br />stock: IBM","theoretical:  1.485063080<br />sample:  1.8599067946<br />change:  1.859907e+00<br />stock: IBM","theoretical:  1.488346886<br />sample:  1.8628968003<br />change:  1.862897e+00<br />stock: IBM","theoretical:  1.491646821<br />sample:  1.8684491462<br />change:  1.868449e+00<br />stock: IBM","theoretical:  1.494963079<br />sample:  1.8719479714<br />change:  1.871948e+00<br />stock: IBM","theoretical:  1.498295860<br />sample:  1.8919683042<br />change:  1.891968e+00<br />stock: IBM","theoretical:  1.501645367<br />sample:  1.9027118552<br />change:  1.902712e+00<br />stock: IBM","theoretical:  1.505011807<br />sample:  1.9057100542<br />change:  1.905710e+00<br />stock: IBM","theoretical:  1.508395390<br />sample:  1.9162611730<br />change:  1.916261e+00<br />stock: IBM","theoretical:  1.511796330<br />sample:  1.9210359710<br />change:  1.921036e+00<br />stock: IBM","theoretical:  1.515214847<br />sample:  1.9291307126<br />change:  1.929131e+00<br />stock: IBM","theoretical:  1.518651164<br />sample:  1.9555803727<br />change:  1.955580e+00<br />stock: IBM","theoretical:  1.522105507<br />sample:  1.9588449835<br />change:  1.958845e+00<br />stock: IBM","theoretical:  1.525578109<br />sample:  1.9596683039<br />change:  1.959668e+00<br />stock: IBM","theoretical:  1.529069205<br />sample:  1.9654264697<br />change:  1.965426e+00<br />stock: IBM","theoretical:  1.532579038<br />sample:  1.9665068061<br />change:  1.966507e+00<br />stock: IBM","theoretical:  1.536107853<br />sample:  1.9757372970<br />change:  1.975737e+00<br />stock: IBM","theoretical:  1.539655901<br />sample:  1.9858643066<br />change:  1.985864e+00<br />stock: IBM","theoretical:  1.543223437<br />sample:  1.9910000429<br />change:  1.991000e+00<br />stock: IBM","theoretical:  1.546810723<br />sample:  1.9946268339<br />change:  1.994627e+00<br />stock: IBM","theoretical:  1.550418026<br />sample:  2.0085745043<br />change:  2.008575e+00<br />stock: IBM","theoretical:  1.554045617<br />sample:  2.0104189107<br />change:  2.010419e+00<br />stock: IBM","theoretical:  1.557693775<br />sample:  2.0124577268<br />change:  2.012458e+00<br />stock: IBM","theoretical:  1.561362783<br />sample:  2.0263827135<br />change:  2.026383e+00<br />stock: IBM","theoretical:  1.565052930<br />sample:  2.0305103298<br />change:  2.030510e+00<br />stock: IBM","theoretical:  1.568764514<br />sample:  2.0313504253<br />change:  2.031350e+00<br />stock: IBM","theoretical:  1.572497834<br />sample:  2.0325552962<br />change:  2.032555e+00<br />stock: IBM","theoretical:  1.576253202<br />sample:  2.0502306738<br />change:  2.050231e+00<br />stock: IBM","theoretical:  1.580030931<br />sample:  2.0531568985<br />change:  2.053157e+00<br />stock: IBM","theoretical:  1.583831345<br />sample:  2.0574649766<br />change:  2.057465e+00<br />stock: IBM","theoretical:  1.587654774<br />sample:  2.0600341282<br />change:  2.060034e+00<br />stock: IBM","theoretical:  1.591501553<br />sample:  2.0695451427<br />change:  2.069545e+00<br />stock: IBM","theoretical:  1.595372028<br />sample:  2.0729223258<br />change:  2.072922e+00<br />stock: IBM","theoretical:  1.599266552<br />sample:  2.0816309984<br />change:  2.081631e+00<br />stock: IBM","theoretical:  1.603185484<br />sample:  2.0853931606<br />change:  2.085393e+00<br />stock: IBM","theoretical:  1.607129194<br />sample:  2.0930869323<br />change:  2.093087e+00<br />stock: IBM","theoretical:  1.611098059<br />sample:  2.1027653287<br />change:  2.102765e+00<br />stock: IBM","theoretical:  1.615092465<br />sample:  2.1426395883<br />change:  2.142640e+00<br />stock: IBM","theoretical:  1.619112808<br />sample:  2.1440743873<br />change:  2.144074e+00<br />stock: IBM","theoretical:  1.623159493<br />sample:  2.1487081025<br />change:  2.148708e+00<br />stock: IBM","theoretical:  1.627232934<br />sample:  2.1500159716<br />change:  2.150016e+00<br />stock: IBM","theoretical:  1.631333556<br />sample:  2.1543606567<br />change:  2.154361e+00<br />stock: IBM","theoretical:  1.635461794<br />sample:  2.1665148364<br />change:  2.166515e+00<br />stock: IBM","theoretical:  1.639618093<br />sample:  2.1675259977<br />change:  2.167526e+00<br />stock: IBM","theoretical:  1.643802912<br />sample:  2.1697700619<br />change:  2.169770e+00<br />stock: IBM","theoretical:  1.648016717<br />sample:  2.1734890516<br />change:  2.173489e+00<br />stock: IBM","theoretical:  1.652259990<br />sample:  2.1752435775<br />change:  2.175244e+00<br />stock: IBM","theoretical:  1.656533223<br />sample:  2.1839121051<br />change:  2.183912e+00<br />stock: IBM","theoretical:  1.660836920<br />sample:  2.1841691083<br />change:  2.184169e+00<br />stock: IBM","theoretical:  1.665171601<br />sample:  2.1972084534<br />change:  2.197208e+00<br />stock: IBM","theoretical:  1.669537798<br />sample:  2.1979811819<br />change:  2.197981e+00<br />stock: IBM","theoretical:  1.673936056<br />sample:  2.2060645699<br />change:  2.206065e+00<br />stock: IBM","theoretical:  1.678366937<br />sample:  2.2240310007<br />change:  2.224031e+00<br />stock: IBM","theoretical:  1.682831015<br />sample:  2.2495023129<br />change:  2.249502e+00<br />stock: IBM","theoretical:  1.687328883<br />sample:  2.2749782755<br />change:  2.274978e+00<br />stock: IBM","theoretical:  1.691861149<br />sample:  2.2946434722<br />change:  2.294643e+00<br />stock: IBM","theoretical:  1.696428436<br />sample:  2.3089683897<br />change:  2.308968e+00<br />stock: IBM","theoretical:  1.701031388<br />sample:  2.3192034636<br />change:  2.319203e+00<br />stock: IBM","theoretical:  1.705670665<br />sample:  2.3312810532<br />change:  2.331281e+00<br />stock: IBM","theoretical:  1.710346946<br />sample:  2.3332651095<br />change:  2.333265e+00<br />stock: IBM","theoretical:  1.715060931<br />sample:  2.3492622012<br />change:  2.349262e+00<br />stock: IBM","theoretical:  1.719813337<br />sample:  2.3578059898<br />change:  2.357806e+00<br />stock: IBM","theoretical:  1.724604907<br />sample:  2.3784818720<br />change:  2.378482e+00<br />stock: IBM","theoretical:  1.729436403<br />sample:  2.4060661565<br />change:  2.406066e+00<br />stock: IBM","theoretical:  1.734308610<br />sample:  2.4109392427<br />change:  2.410939e+00<br />stock: IBM","theoretical:  1.739222339<br />sample:  2.4565054795<br />change:  2.456505e+00<br />stock: IBM","theoretical:  1.744178422<br />sample:  2.4634663052<br />change:  2.463466e+00<br />stock: IBM","theoretical:  1.749177722<br />sample:  2.4690428738<br />change:  2.469043e+00<br />stock: IBM","theoretical:  1.754221125<br />sample:  2.4708893700<br />change:  2.470889e+00<br />stock: IBM","theoretical:  1.759309548<br />sample:  2.4710888430<br />change:  2.471089e+00<br />stock: IBM","theoretical:  1.764443934<br />sample:  2.4751193563<br />change:  2.475119e+00<br />stock: IBM","theoretical:  1.769625261<br />sample:  2.4908633695<br />change:  2.490863e+00<br />stock: IBM","theoretical:  1.774854535<br />sample:  2.5047680758<br />change:  2.504768e+00<br />stock: IBM","theoretical:  1.780132799<br />sample:  2.5058745919<br />change:  2.505875e+00<br />stock: IBM","theoretical:  1.785461129<br />sample:  2.5074085670<br />change:  2.507409e+00<br />stock: IBM","theoretical:  1.790840637<br />sample:  2.5120799758<br />change:  2.512080e+00<br />stock: IBM","theoretical:  1.796272476<br />sample:  2.5140586062<br />change:  2.514059e+00<br />stock: IBM","theoretical:  1.801757836<br />sample:  2.5317171735<br />change:  2.531717e+00<br />stock: IBM","theoretical:  1.807297952<br />sample:  2.5448688627<br />change:  2.544869e+00<br />stock: IBM","theoretical:  1.812894101<br />sample:  2.5490315390<br />change:  2.549032e+00<br />stock: IBM","theoretical:  1.818547608<br />sample:  2.5643073626<br />change:  2.564307e+00<br />stock: IBM","theoretical:  1.824259843<br />sample:  2.5778285040<br />change:  2.577829e+00<br />stock: IBM","theoretical:  1.830032232<br />sample:  2.5889965771<br />change:  2.588997e+00<br />stock: IBM","theoretical:  1.835866250<br />sample:  2.5931986032<br />change:  2.593199e+00<br />stock: IBM","theoretical:  1.841763431<br />sample:  2.6077876886<br />change:  2.607788e+00<br />stock: IBM","theoretical:  1.847725366<br />sample:  2.6100176396<br />change:  2.610018e+00<br />stock: IBM","theoretical:  1.853753712<br />sample:  2.6410774949<br />change:  2.641077e+00<br />stock: IBM","theoretical:  1.859850187<br />sample:  2.6559514790<br />change:  2.655951e+00<br />stock: IBM","theoretical:  1.866016582<br />sample:  2.6636121397<br />change:  2.663612e+00<br />stock: IBM","theoretical:  1.872254759<br />sample:  2.6895905109<br />change:  2.689591e+00<br />stock: IBM","theoretical:  1.878566656<br />sample:  2.7068333086<br />change:  2.706833e+00<br />stock: IBM","theoretical:  1.884954295<br />sample:  2.7142842627<br />change:  2.714284e+00<br />stock: IBM","theoretical:  1.891419784<br />sample:  2.7367803372<br />change:  2.736780e+00<br />stock: IBM","theoretical:  1.897965319<br />sample:  2.7374939341<br />change:  2.737494e+00<br />stock: IBM","theoretical:  1.904593195<br />sample:  2.7670352381<br />change:  2.767035e+00<br />stock: IBM","theoretical:  1.911305810<br />sample:  2.7758630776<br />change:  2.775863e+00<br />stock: IBM","theoretical:  1.918105668<br />sample:  2.8024505893<br />change:  2.802451e+00<br />stock: IBM","theoretical:  1.924995390<br />sample:  2.8043594393<br />change:  2.804359e+00<br />stock: IBM","theoretical:  1.931977719<br />sample:  2.8164228268<br />change:  2.816423e+00<br />stock: IBM","theoretical:  1.939055529<br />sample:  2.8231355433<br />change:  2.823136e+00<br />stock: IBM","theoretical:  1.946231830<br />sample:  2.8307727273<br />change:  2.830773e+00<br />stock: IBM","theoretical:  1.953509784<br />sample:  2.8478051118<br />change:  2.847805e+00<br />stock: IBM","theoretical:  1.960892708<br />sample:  2.8673265750<br />change:  2.867327e+00<br />stock: IBM","theoretical:  1.968384089<br />sample:  2.9086238438<br />change:  2.908624e+00<br />stock: IBM","theoretical:  1.975987595<br />sample:  2.9224554230<br />change:  2.922455e+00<br />stock: IBM","theoretical:  1.983707085<br />sample:  2.9511397548<br />change:  2.951140e+00<br />stock: IBM","theoretical:  1.991546628<br />sample:  2.9765312233<br />change:  2.976531e+00<br />stock: IBM","theoretical:  1.999510515<br />sample:  3.0155364922<br />change:  3.015536e+00<br />stock: IBM","theoretical:  2.007603274<br />sample:  3.0508461356<br />change:  3.050846e+00<br />stock: IBM","theoretical:  2.015829694<br />sample:  3.0530282559<br />change:  3.053028e+00<br />stock: IBM","theoretical:  2.024194838<br />sample:  3.0719382603<br />change:  3.071938e+00<br />stock: IBM","theoretical:  2.032704074<br />sample:  3.0847916108<br />change:  3.084792e+00<br />stock: IBM","theoretical:  2.041363088<br />sample:  3.1341245366<br />change:  3.134125e+00<br />stock: IBM","theoretical:  2.050177922<br />sample:  3.1666164976<br />change:  3.166616e+00<br />stock: IBM","theoretical:  2.059154998<br />sample:  3.1897015127<br />change:  3.189702e+00<br />stock: IBM","theoretical:  2.068301150<br />sample:  3.2400928856<br />change:  3.240093e+00<br />stock: IBM","theoretical:  2.077623666<br />sample:  3.2744259079<br />change:  3.274426e+00<br />stock: IBM","theoretical:  2.087130323<br />sample:  3.2885959580<br />change:  3.288596e+00<br />stock: IBM","theoretical:  2.096829437<br />sample:  3.3455087803<br />change:  3.345509e+00<br />stock: IBM","theoretical:  2.106729912<br />sample:  3.3557025175<br />change:  3.355703e+00<br />stock: IBM","theoretical:  2.116841300<br />sample:  3.3589203415<br />change:  3.358920e+00<br />stock: IBM","theoretical:  2.127173863<br />sample:  3.4094210481<br />change:  3.409421e+00<br />stock: IBM","theoretical:  2.137738647<br />sample:  3.4152323376<br />change:  3.415232e+00<br />stock: IBM","theoretical:  2.148547566<br />sample:  3.4169449828<br />change:  3.416945e+00<br />stock: IBM","theoretical:  2.159613493<br />sample:  3.4393590710<br />change:  3.439359e+00<br />stock: IBM","theoretical:  2.170950371<br />sample:  3.4450150815<br />change:  3.445015e+00<br />stock: IBM","theoretical:  2.182573337<br />sample:  3.4475191538<br />change:  3.447519e+00<br />stock: IBM","theoretical:  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What About Dash?

Dash for R is an open-source framework for building analytical applications, with no Javascript required, and it is tightly integrated with the Plotly graphing library.

Learn about how to install Dash for R at https://dashr.plot.ly/installation.

Everywhere in this page that you see fig, you can display the same figure in a Dash for R application by passing it to the figure argument of the Graph component from the built-in dashCoreComponents package like this:

library(plotly)

fig <- plot_ly() 
# fig <- fig %>% add_trace( ... )
# fig <- fig %>% layout( ... ) 

library(dash)
library(dashCoreComponents)
library(dashHtmlComponents)

app <- Dash$new()
app$layout(
    htmlDiv(
        list(
            dccGraph(figure=fig) 
        )
     )
)

app$run_server(debug=TRUE, dev_tools_hot_reload=FALSE)